A bibliography on asymptotic safety

Last update January 2020

Papers on asymptotic safety of gravity
Applications of asymptotically safe gravity
Other nonperturbatively renormalizable theories and applications
Classic papers on quantum gravity
Euclidean quantum gravity
Effective field theory of gravity
Discrete gravity
Gravitational effects on matter couplings
Other relevant papers

Papers on asymptotic safety of gravity.


Steven Weinberg (1976)

Critical Phenomena for Field Theorists.

Lectures presented at Int. School of Subnuclear Physics, Ettore Majorana, Erice, Sicily, Jul 23 - Aug 8, 1976.
Published in Erice Subnucl. Phys.1976:1

Preprint version


S.M. Christensen and Michael J. Duff (1978).

Quantum Gravity In Two + Epsilon Dimensions,

Phys. Lett. B 79, 213.


R. Gastmans, R. Kallosh and C. Truffin (1978).

Quantum Gravity Near Two-Dimensions,

Nucl. Phys. B 133, 417.


In these two papers, the beta function of Newton’s constant is computed using the ε expansion around two dimensions.

Steven Weinberg (1979)

Ultraviolet divergences in quantum theories of gravitation.

In "General Relativity: An Einstein centenary survey", ed. S. W. Hawking and W. Israel, chapter 16, pp.790--831; Cambridge University Press.


The term "Asymptotic Safety" was introduced in this paper to characterize a class of theories that have a good ultraviolet limit and are predictive. The condition for this to happen is that there exists a fixed point with finitely many UV attractive directions. Based on results of the ε expansion around two dimensions, it was suggested that gravity may be asymptotically safe.


Lee Smolin (1982)

A fixed point for quantum gravity.

Nucl. Phys. B 208, 439-466


It was shown in this paper that a fixed point must exist in 4-d gravity in the leading order of a 1/N approximation.


Hikaru Kawai and Masao Ninomiya (1990)

Renormalization group and quantum gravity.

Nuclear Physics B 336, 115-145


This paper discusses several issues related to the application of the renormalization group to quantum gravity, in particular in relation to the ε expansion. It is observed that due to its nontrivial dimensionality, the running of Newton’s constant must be compared to that of some other reference operator, and several options are discussed. The appearance of kinematical poles in the graviton propagator at ε=0  is noted, and possible cures proposed. The fractal nature of spacetime is also discussed.


I. Jack, D.R.T. Jones (1991)

The Epsilon expansion of two-dimensional quantum gravity.

Nucl.Phys.B358, 695-712


Hikaru Kawai, Yoshihisa Kitazawa, Masao Ninomiya (1993a)

Scaling exponents in quantum gravity near two-dimensions.

Nucl. Phys. B393, 280-300



Hikaru Kawai, Yoshihisa Kitazawa, Masao Ninomiya (1993b)

Ultraviolet stable fixed point and scaling relations in (2+epsilon)-dimensional quantum gravity.

Nucl. Phys. B404, 684-716



Toshiaki Aida, Yoshihisa Kitazawa, Hikaru Kawai, Masao Ninomiya (1994)

Conformal invariance and renormalization group in quantum gravity near two-dimensions.

Nucl. Phys. B427, 158-180



Jun Nishimura, Shinya Tamura, Asato Tsuchiya (1994)

R**2 gravity in (2+epsilon)-dimensional quantum gravity.

Mod. Phys. Lett. A9, 3565-3574



Hikaru Kawai, Yoshihisa Kitazawa, Masao Ninomiya (1996)

Renormalizability of quantum gravity near two-dimensions.

Nucl. Phys. B467, 313-331



T. Aida and Y. Kitazawa (1997)

Two--loop prediction for scaling exponents in (2+ε)--dimensional quantum gravity.

Nucl. Phys. B 491, 427. 



This series of papers elaborate on the issues raised in Kawai and Ninomiya 1990. In particular Kawai, Kitazawa, Ninomiya (1993a,b) and Aida, Kitazawa, Kawai, Ninomiya (1994) discuss the choice of the conformal factor as a reference operator.


Martin Reuter (1996)

Nonperturbative evolution equation for quantum gravity.

Phys. Rev. D57, 971.



In this paper the ERGE is written for gravity. It is then truncated and the beta functions for Newton's constant and the cosmological constant are derived in d dimensions, where d can be equal to 4. Due to the choice of exponential cutoff function, they are left in the form of (manifestly convergent but not calculable in closed form) integrals over momenta. The results are compared numerically with the calculations in 2+ ε dimensions, and with calculations of the quantum correction to the Newtonian potential (by Donoghue 1994, Hamber and Liu 1995).


Djamel Dou and Roberto Percacci (1998)

The running gravitational couplings.

Class. Quant. Grav. 15, 3449



In this paper the results of Reuter 1998 are rederived using a slightly different method and adding the contribution of minimally coupled matter fields.


L.N. Granda, Sergei D. Odintsov (1997)

Exact renormalization group for O(4) gauged supergravity.

Phys. Lett. B409 206-212



The beta functions of Reuter 1998 are written for N=4 supergravity. The cutoff procedure does not respect supersymmetry and therefore if one starts at a supersymmetric initial value, the flow will immediately lead to a non supersymmetric theory. It is observed that the beta functions admit a nontrivial fixed point.


A.A. Bytsenko, L.N. Granda, Sergei D. Odintsov (1997)

Exact renormalization group and running Newtonian coupling in higher derivative gravity.

JETP Lett. 65, 600-604



Here, using the ERGE, the effect of an R2 term on the running of Newton's constant is computed.(The running of the R2 term is not calculated.


L.N. Granda, Sergei D. Odintsov (1998)

Effective average action and nonperturbative renormalization group equation in higher derivative quantum gravity.

Grav. Cosmol. 4, 85-95



The beta function of a term η R2 is computed starting from the Einstein-Hilbert truncation of the action. The contribution of the coupling η to its own beta function is not taken into account.


Sven Falkenberg, Sergei D. Odintsov (1998)

Gauge dependence of the effective average action in Einstein gravity.

Int. J. Mod. Phys. A13, 607-623



Talk given at the 8th Marcel Grossmann Meeting.


Wataru Souma (1999)

Nontrivial ultraviolet fixed point in quantum gravity.

Prog. Theor. Phys. 102, 181.



The beta functions of Reuter 1998 are solved numerically and a nontrivial fixed point is found. It is shown that it is UV attractive in both directions.

Wataru Souma (2000)

Gauge and cutoff function dependence of the ultraviolet fixed point in quantum gravity.



Martin Reuter (2000)

Newton's constant isn't constant.

Annual Report 2000 of the International School in Physics and Mathematics, Tbilisi, Georgia.

arXiv: hep-th/0012069


Oliver Lauscher and Martin Reuter (2001)

Ultraviolet fixed point and generalized flow equation of quantum gravity.

Phys. Rev. D65, 025013.



The flow equation is analyzed using the York decomposition, in the Einstein-Hilbert truncation. It is observed that the quantum corrected graviton propagator behaves at high energy as if it was defined in two dimensions.


Martin Reuter and Frank Saueressig (2002a)

Renormalization group flow of quantum gravity in the Einstein--Hilbert truncation.

Phys. Rev. D65, 065016



Contains a detailed discussion of the flow in the Einstein-Hilbert truncation, using a sharp cutoff instead of a smooth cutoff. The flow equations are numerically integrated and types of trajectories are classified.


Oliver Lauscher and Martin Reuter (2002a)

Towards nonperturbative renormalizability of quantum Einstein gravity.

Int. J. Mod. Phys. A 17, 993.



Talk given at 5th Workshop on Quantum Field Theory Under the Influence of External Conditions, Leipzig, Germany, 10-14 Sep 2001.


Oliver Lauscher and Martin Reuter (2002b)

Flow equation of quantum Einstein gravity in a higher derivative truncation.

Phys. Rev. D 66, 025026.



Here the ERGE is applied to a truncation involving a term η R2 (where η  is a dimensionless coupling). The standard De Donder gauge is used with α=1. It is found that the nontrivial fixed point still exists, with values of the cosmological constant and Newton's constant that are only slightly shifted with respect to the Einstein-Hilbert truncation. η is small. The Gaussian fixed point does not exists in this parametrization (it corresponds to 1/ η =0).


Oliver Lauscher and Martin Reuter (2002c)

Is quantum Einstein gravity nonperturbatively renormalizable?

Class. Quant. Grav. 19, 483.



A summary of then-current evidence for asymptotic safety.


Martin Reuter, Frank Saueressig (2002b)

A Class of nonlocal truncations in quantum Einstein gravity and its renormalization group behavior.

Phys. Rev. D66, 125001



Contains an analysis of actions that contain the Einstein-Hilbert term plus function of the volume.


Roberto Percacci and Daniele Perini (2002)

Constraints on matter from asymptotic safety.

Phys. Rev. D67, 081503 (R).



It is shown that the existence of a FP can place constraints on the type and number of matter fields. Gravity is treated in the Einstein-Hilbert truncation and the matter fields are minimally coupled. The fermions are treated by imposing a so-called "type I" cutoff on the square of the Dirac operator. This gives rise to issues that are discussed in Dona' and Percacci 2012.


Peter Forgacs, Max Niedermaier (2002)

A Fixed point for truncated quantum Einstein gravity.



Max Niedermaier (2002)

On the renormalization of truncated quantum Einstein gravity.

JHEP 0212, 066



Instead of keeping all the degrees of freedom of the metric and truncating the action, in these papers gravity is simplified by considering only metrics with two Killing vectors, while retaining the most general action. Asymptotic safety of the resulting theory is discussed.


Roberto Percacci and Daniele Perini (2003)

Asymptotic safety of gravity coupled to matter.

Phys. Rev. D68, 044018 .



Same general setup as Percacci and Perini 2002, but here one scalar field is allowed to have arbitrary potential V and interactions F R where F is a function of the scalar field. It is observed that there are models with nontrivial V and F where all scalar interactions are asymptotically free. The formulae for the beta functions contain many misprints. For correct and more explicit formulae see the appendix of Narain and Percacci 2009b.


Max Niedermaier (2003)

Dimensionally reduced gravity theories are asymptotically safe.

Nucl. Phys. B 673, 131-169.



Martin Reuter, Frank Saueressig (2004)

Nonlocal quantum gravity and the size of the universe. 

Fortsch. Phys. 52, 650-654



Talk given at 36th International Symposium Ahrenshoop on the Theory of Elementary Particles: Recent Developments in String M Theory and Field Theory, Wernsdorf, Germany, 26-30 Aug 2003.


Daniel F. Litim (2004)

Fixed points of quantum gravity.

Phys. Rev. Lett. 92, 201301.



By means of a clever choice of cutoff function, closed expressions are given for the beta functions of the cosmological constant and Newton's constant.


Roberto Percacci and Daniele Perini (2004)

On the ultraviolet behaviour of Newton's constant.

Class. and Quantum Grav. 21, 5035.



This paper discusses an apparent puzzle in asymptotically safe gravity. It is noted that Newton's constant can be eliminated by a rescaling of the metric. It seems therefore to be a redundant coupling, in which case asymptotic safety would not require that is approaches a FP in the UV limit  Why is it then that in the calculations Newton's constant seems to have a FP? The answer is related to the fact that the cutoff k cannot be eliminated simultaneously with G.


Alfio Bonanno, Martin Reuter (2005)

Proper time flow equation for gravity.

JHEP 0502, 035



The proper time form of the RG for gravity is analyzed; results are compared to those obtained from the ERGE.


Oliver Lauscher and Martin Reuter (2005)

Fractal spacetime structure in asymptotically safe gravity.

JHEP 0510, 050



This paper discusses the short distance geometry of spacetime in an asymptotically safe theory of gravity. Aside from the argument about the UV behaviour of the graviton propagator, given already in Lauscher and Reuter (2002a), it argued that any propagator will behave in momentum space like p-4.The possible relation with the results of Ambjørn et al (2005a)  is also discussed.


Martin Reuter and Jan-Markus Schwindt (2006)

A Minimal length from the cutoff modes in asymptotically safe quantum gravity.

JHEP 0601, 070



This paper discusses the quantum 4-sphere as a specific example of a fractal spacetime manifold.


Oliver Lauscher, Martin Reuter (2005)

Asymptotic safety in quantum Einstein gravity: Nonperturbative renormalizability and fractal spacetime structure.

In “Quantum gravity” , ed. B. Fauser, J. Tolksdorf and E. Zeidler, p.293-313. 



Invited talk at 14th Oporto Meeting on Geometry, Topology and Physics: Mathematical Aspects of Quantum Field Theory, Oporto, Portugal, 21-24 Jul 2005.


Roberto Percacci (2006)

Further evidence for a gravitational fixed point.

Phys. Rev. D73, 041501(R).



The approximation of Tomboulis (1977) is applied in the context of the ERGE. It is shown that in the leading order of the 1/N approximation a fixed point exists for all couplings in a derivative expansion of the action. It is also shown that with the optimized cutoff of Litim (2001) all the coefficients of terms with six or more derivatives of the metric are zero at the FP.


Max Niedermaier, Martin Reuter (2006)

The Asymptotic Safety Scenario in Quantum Gravity



An extensive review of the notion of asymptotic safety and its application to gravity.


Peter Fischer, Daniel F. Litim (2006)

Fixed points of quantum gravity in extra dimensions.

Phys. Lett. B638, 497-502 (2006).



The FP is shown to exist also in dimensions greater that four. The asymptotic safety scenario can therefore be applied also in models with extra dimensions.


Daniel F. Litim (2006)

On fixed points of quantum gravity.

AIP Conf. Proc. 841, 322-329 (2006).
Also in *Oviedo 2006, A century of relativity physics* 322-329



Talk presented at 28th Spanish Relativity Meeting (ERE05): A Century of Relativity Physics, Oviedo, Asturias, Spain, 6-10 Sep 2005.


Peter Fischer, Daniel F. Litim (2006)

Fixed points of quantum gravity in higher dimensions.

AIP Conf. Proc. 861, 336-343 (2006).
Also in *Paris 2005, Albert Einstein's century* 336-343



Talk presented at Albert Einstein's Century International Conference, Paris, France, 18-22 Jul 2005.


Max Niedermaier (2007)

The Asymptotic safety scenario in quantum gravity: An Introduction.

Class. Quant. Grav. 24, R171 (2007).



Roberto Percacci (2007a)

The renormalization group, systems of units and the hierarchy problem.

J. Phys. A40, 4895-4914



This paper contains a detailed discussion of the role of field rescalings in the definition of RG transformations. It is shown that the rescalings associated to a choice of units lead to a scale-dependent metric that reproduces the geometry of anti de Sitter space. Connection with the Randall-Sundrum scenario is pointed out.


Alessandro Codello, Roberto Percacci (2006)

Fixed points of higher derivative gravity.

Phys. Rev. Lett. 97, 221301



This paper establishes a link between old literature on higher derivative gravity (references given below) and the approach to asymptotic safety based on the ERGE. It contains a one loop recalculation of the beta functions of a theory containing arbitrary terms with up to four derivatives of the metric. The old results are reproduced for the dimensionless couplings, but in the case of Newton's constant and cosmological constant some new terms appear. They produce a nontrivial FP for these couplings.


Martin Reuter and Jan-Markus Schwindt (2007a)

Scale-dependent metric and causal structures in Quantum Einstein Gravity.

JHEP 0701, 049



This paper analyzes various conceptual issues related to the scale dependence of the metric.


Martin Reuter, Jan-Markus Schwindt (2007b)

Scale Dependent Metric and Minimal Length in QEG.

J. Phys. A40, 6595-6606



In the Proceedings of IRGAC 2006. Discusses the possibility of a minimal length in asymptotically safe quantum Einstein gravity.


Alessandro Codello, Roberto Percacci, Christoph Rahmede (2007)

Ultraviolet properties of f(R)-gravity.

Int. J. Mod. Phys. A23, 143-150

arXiv:0705.1769 [hep-th]


Computes the beta functions in a truncation involving powers of the Ricci scalar. The calculation is drastically simplified by a choice of gauge and cutoff. In this trucation the critical surface can be computed explicitly and has dimension three.


Martin Reuter and Frank Saueressig (2007)

Functional Renormalization Group Equations, Asymptotic Safety, and Quantum Einstein Gravity.

arXiv:0708.1317 [hep-th]


Lectures given at First Quantum Geometry and Quantum Gravity School, Zakopane, Poland, 23 Mar - 3 Apr 2007.


Roberto Percacci (2007)

Asymptotic Safety.

arXiv:0709.3851 [hep-th]


In 'Approaches to Quantum Gravity: Toward a New Understanding of Space, Time and Matter' ed. D. Oriti, Cambridge University Press. (2009)


Pedro F. Machado and Frank Saueressig (2007)

On the renormalization group flow of f(R)-gravity.

Phys. Rev. D77, 124045

arXiv:0712.0445 [hep-th]


Rederives and extends the results of Codello, Percacci and Rahmede (2007). In addition to polynomials in R also considers Lagrangians that are logarithmic in R or inverse powers of R. In some cases a nontrivial IR attractor is also found.


Martin Reuter and Holger Weyer (2008a)

Background independence and asymptotic safety in conformally reduced gravity
Phys. Rev. D79, 105005 (2009)

arXiv:0801:3287 [hep-th]


This paper discusses the RG flow in conformally reduced gravity, meaning that only the conformal degree of freedom is retained. There is a detailed discussion of the proper way of defining the cutoff in such a theory, where the role of “background independence” is emphasized. It is shown that, perhaps surprisingly, this reduced dynamics by itself has a fixed point for Newton’s constant and the cosmological constant, which is very similar to the one of the full theory.


Martin Reuter and Holger Weyer (2008b)

Conformal sector of Quantum Einstein Gravity in the local potential approximation: non-Gaussian fixed point and a phase of diffeomorphism invariance.

Phys. Rev. D80, 025001,2009.

arXiv:0804:1475 [hep-th]


This paper continues the exploration of conformally reduced gravity. Here the truncation of the action contains an arbitrary potential for the conformal factor; this would derive also from terms in the action containing inverse powers of R. There is a discussion of the fact that the running potential may switch from a symmetric phase (minimum at zero) to a broken symmetry phase (nonzero minimum). The results depend partly on the topology; the problem is discussed in flat space and on the sphere.


Alessandro Codello, Roberto Percacci, Christoph Rahmede (2008)

Investigating the ultraviolet properties of gravity with a Wilsonian renormalization group equation

Ann. Phys. 324, 414-469 (2009)



This paper contains a detailed account of work announced briefly in Codello and Percacci (2006), Codello et al (2007). In addition it contains an extended discussion of various ways of defining the cutoff, beta functions for the Einstein-Hilbert truncation for all these cutoff types, and a discussion about the role of divergences in an asymptotically safe theory, in particular calculations reproducing the known one loop divergences.


Jan-Eric Daum, Martin Reuter (2008)

Effective Potential of the Conformal Factor: Gravitational Average Action and Dynamical Triangulations

Adv. Sci. Lett. 2, 255 (2009)

arXiv:0806.3907 [hep-th]


This paper establishes a possible point of contact between asymptotic safety and causal dynamical triangulations. It is shown that in an asymptotically safe theory, the effective potential for the conformal factor has vanishing derivative at the origin. The same property seems to hold for the effective potential of the scale factor in a dynamically triangulated Robertson Walker universe.


Daniel F. Litim (2008)

Fixed Points of Quantum Gravity and the Renormalisation Group.

In the proceedings of "From Quantum to Emergent Gravity: Theory and Phenomenology", June 11-15 2007, Trieste, Italy

arXiv:0810.3675 [hep-th]


Elisa Manrique and Martin Reuter (2008)

Bare Action and Regularized Functional Integral of Asymptotically Safe Quantum Gravity

Phys. Rev. D79, 025008 (2009).

arXiv:0811.3888 [hep-th]


In the literature listed above, using the ERGE to establish the existence of a fixed point in the flow of the average effective action, there is no need to discuss ultraviolet regulators because the beta functions are automatically finite. Consequently, the relation between the running of the average effective action as a function of the IR cutoff, and the running of the bare action as a function of the UV cutoff is never discussed. To some extent this is not necessary, since asymptotic safety imposes conditions on the effective action, and then only indirectly on the bare one.

This paper describes the construction of an UV-regulated functional integral and a flow equation for the bare action such that the resulting average effective action obeys the ERGE. It is shown that the bare action need not even have a fixed point for the average effective action to have one.


Dario Benedetti, Pedro F. Machado and Frank Saueressig (2009a)

Asymptotic safety in higher-derivative gravity.

Mod. Phys. Lett. A24, 2233-2241

arXiv:0901.2984 [hep-th]


Here the ERGE is applied to a four-parameter truncation containing R2 and Weyl2 terms. No further approximation is made. Unlike in the one loop approximation, the couplings that multiply the higher derivative terms are not asymptotically free, but have finite limits. Two of the critical exponents are very close to the results of the Einstein-Hilbert truncation; the other two are rather large and have opposite signs. The critical surface is therefore three dimensional.


Dario Benedetti, Pedro F. Machado and Frank Saueressig (2009b)

Taming perturbative divergences in asymptotically safe gravity

Nucl. Phys. B824, 168-191 (2010).

arXiv:0902.4630 [hep-th]


In this paper the setup is similar to the previous one, but there is an additional minimally coupled scalar field. The reason why this is significant is that the appearance of curvature squared divergences in Einstein theory at one loop, in the presence of a scalar field, signals nonrenormalizability(‘t Hooft and Veltman). By proving that this truncation admits a nontrivial fixed point, the authors show that nonrenormalizable divergences have no effect on the behavior of the RG flow, as seen using nonperturbative tools.


Steven Weinberg (2009a)

Living with infinities.

arXiv:0903.0568 [hep-th]


Reviews in a historical perspective the problem of infinities in quantum field theory, and how it may be resolved by asymptotic safety.


Martin Reuter and Holger Weyer (2008b)

The role of Background Independence for Asymptotic Safety in Quantum Einstein Gravity.

Gen. Rel. Grav. 41, 983-1011 (2009)

arXiv:0903:2971 [hep-th]


Talk given by M.R. at the WE-Heraeus-Seminar "Quantum Gravity: Challenges and Perspectives", Bad Honnef, April 14-16, 2008


Pedro F. Machado and Roberto Percacci (2009)

Conformally reduced quantum gravity revisited.

Phys. Rev. D80, 024020

arXiv:0904.2510 [hep-th]


Compute the beta functions of conformally reduced gravity in a truncation including terms up to R^2, plus the nonlocal term that generates the conformal anomaly. Various cutoff choices are used, either maintaining or breaking Weyl invariance. With the Weyl breaking cutoff, results of Antoniadis and Mottola (1991) are reproduced.


Elisa Manrique and Martin Reuter (2009a)

Bare vs. Effective Fixed Point Action in Asymptotic Safety: The Reconstruction Problem.

PoS CLAQG08 (2011) 001
arXiv:0905.4220 [hep-th]

Talk given by M.R. at the Workshop on Continuum and Lattice Approaches to Quantum Gravity. Sept. 2008, Brighton UK


Astrid Eichhorn, Holger Gies, Michael M. Scherer (2009)

Asymptotically free scalar curvature-ghost coupling in Quantum Einstein Gravity.

Phys. Rev. D80, 104003 (2009)

arXiv:0907.1828 [hep-th]


A new coupling is introduced in the ghost sector and is found to be asymptotically free and relevant.


Elisa Manrique and Martin Reuter (2009b)

Bimetric Truncations for Quantum Einstein Gravity and Asymptotic Safety.

Annals Phys. 325 785-815 (2010)

arXiv:0907.2617 [hep-th]


The effective gravitational action obeying the ERGE depends on two metrics (the background metric and the expectation value of the quantum metric). Previous studies had concentrated on a restricted function space in which the two metrics are identified. Here the authors consider a simple truncation with separate dependence on the two metrics. A fixed point is found, but with some interesting differences relative to previously studied cases.


Steven Weinberg (2009b)

Effective Field Theory, Past and Future.
PoS CD09, 001 (2009)

arXiv:0908.1964 [hep-th]


Reviews in a historical perspective the shifting point of view on the meaning of quantum field theory, and discusses asymptotic safety in this light.


Dario Benedetti, Pedro F. Machado and Frank Saueressig (2009b)

Four-derivative interactions in asymptotically safe gravity

arXiv:0909.3265 [hep-th]


In the Proceedings of the XXV Max Born Symposium "The Planck Scale", Wroclaw, 29 June - 3 July, 2009


Gaurav Narain and Roberto Percacci (2009a)

On the scheme dependence of gravitational beta functions.
Acta phys, Polon. B40 3439-3457 (2009)
arXiv:0910.5390 [hep-th]

In  the Proceedings of the 49-th Cracow School of Theoretical Physics, "Non-perturbative Gravity and Quantum Chromodynamics", May 31-June 10, 2009

Gaurav Narain and Roberto Percacci (2009b)

Renormalization group flow in scalar-tensor theories I.
Class. and Quantum Grav. 27, 075001 (2010)
arXiv:0911.0386 [hep-th]

Gaurav Narain and Christoph Rahmede (2009)

Renormalization group flow in scalar-tensor theories II.
Class. and Quantum Grav. 27, 075002 (2010)

arXiv:0911.0394 [hep-th]

These papers contain a calculation of beta functions for a scalar coupled to gravity. In addition to a kinetic term, the action contains a potential and a nonminimal coupling of the form F(phi)R, in I, and of the more general form F(phi,R) in II.

Max Niedermaier (2009)

Gravitational fixed points from perturbation theory.

Phys. Rev. Lett. 103, 101303 (2009).


Kai Groh and Frank Saueressig(2010)

Ghost wave function renormalization in asymptotically safe quantum gravity.

J. Phys. A43 365403 (2010).

arXiv:1001.5032 [hep-th]


Compute the effect of the ghost anomalous dimension on the running of G and Lambda. The properties of the fixed point are not very different from earlier treatments, but the scheme dependence is less pronounced.


Astrid Eichhorn, Holger Gies (2010)

Ghost anomalous dimension in asymptotically safe quantum gravity.

Phys. Rev. D81, 104010 (2010)

arXiv:1001.5033 [hep-th]


Compute the effect of the ghost anomalous dimension. The difference between this paper and the preceding one is in the

form of the cutoff (here spectrally adjusted). The numerical differences are within the expected cutoff dependence.


Roberto Percacci and Ergin Sezgin (2010)

One Loop Beta Functions in Topologically Massive Gravity.

Class. Quant. Grav. 27 155009 (2010).

arXiv:1002.2640 [hep-th]


Compute the beta functions of topologically massive gravity in 3d and find that the theory is asymptotically safe in perturbation theory.


Elisa Manrique, Martin Reuter and Frank Saueressig (2010a)

Matter induced bimetric actions for gravity.
Ann. Phys. 326, 440-462 (2011)

arXiv:1003.5129 [hep-th]


Here the flow of bimetric actions is calculated in the large N limit.


Elisa Manrique, Martin Reuter and Frank Saueressig (2010b)

Bimetric Renormalization Group Flows in Quantum Einstein Gravity.

Ann. Phys. 326, 463-485 (2011)

arXiv:1006.0099 [hep-th]


This paper continues the work of Manrique and Reuter (2009b) examining the beta functions in the “double Einstein Hilbert”

Truncation, which contains separate cosmological and Einstein terms constructed with the dynamical and background metric.


Max Niedermaier (2010)

Gravitational fixed points and asymptotic safety from perturbation theory.

Nucl. Phys. B833, 226-270 (2010)


A detailed rederivation of the one loop beta functions in Einstein-Hilbert and R^2 gravity truncations. In the latter case the couplings in the R^2 sector are observed to be asymptotically free, in agreement with the one loop calculation of Codello and Percacci (2006), but in disagreement with the FRGE calculation in Benedetti, Machado and Saueressig (2009). The numerical differences in the Lambda-G sector can be attributed to the different gauge and cutoff scheme.


Roberto Percacci and Gian Paolo Vacca (2010)

Asymptotic safety, emergence and minimal length
Class. and Quantum Grav. 27, 245026


This paper shows (1) that asymptotic safety can be seen as an "emergent" property of gravity provided the trajectory is not renormalizable but close to one that is, (2) that under certain circumstances it predicts a minimal length. Some scattering cross sections are calculated and the effect of asymptotic safety is emphasized.

Changjung Gao and Anzhong Wang (2010)

Ghosts and stability of asymptotically safe gravity in the Minkowski background.

arXiv:1010.5955 [gr-qc]

Dario Benedetti, Kai Groh, Pedro F. Machado and Frank Saueressig (2010)

The universal RG machine
JHEP 1106, 079 (2011)

arXiv:1012.3081 [hep-th]


This paper presents a general method for calculating functional traces involving functions of an operator with insertions of another operator, in terms of the off-diagonal heat kernel coefficients. As an example, the machinery is applied to the Einstein-Hilbert truncation.

Jan-Erik Daum and Martin Reuter (2010a)

Renormalization group flow of the Holst action
Phys.Lett. B710 (2012) 215-218

arXiv:1012.4280 [hep-th]


This paper addresses for the first time the issue of asymptotic safety in a first order formulation of gravity, with the connection treated as an independent variable. The action contains, in addition to the usual Palatini term, also a term that does not contribute to the equations of motion having the Immirzi parameter as coefficient.

Jan-Erik Daum and Martin Reuter (2011)

Running Immirzi parameter and asymptotic safety
CNCFG2010, 003 (2010)
arXiv:1111.0991 [hep-th]

Talk given at CORFU 2010.

Alessandro Codello and Omar Zanusso (2011)

Fluid membranes and 2d quantum gravity
Phys. Rev. D83 125021 (2011)

arXiv:1103.1089 [hep-th]

The authors compute the beta functions of a theory of two dimensional surfaces embedded in a D-dimensional Euclidean space. The action contains three terms, corresponding to surface tension, intrinsic curvature and extrinsic curvature. The limit D->0, corresponding to two dimensional gravity, is then studied.
The result differs in interesting ways from the one of Kawai and Ninomiya (1990).

Elisa Manrique, Stefan Rechenberger and Frank Saueressig (2010)

Asymptotically safe Lorentzian gravity
Phys. Rev. Lett. 106 251302 (2011)

arXiv:1102.5012 [hep-th]

The beta functions of Newton's constant and of the cosmological constant are computed using a 3+1 decomposition of the metric which allows the simultaneous treatment of Lorentzian and Euclidean metrics. Time is assumed to be periodic. The results depend on the signature but are nearly indistinguishable in the two cases.

Gian Paolo Vacca and Luca Zambelli (2011)

Functional RG flow equation: regularization and coarse-graining in phase space.

Phys. Rev. D83 125024 (2011)

arXiv:1103.2219 [hep-th]


This paper addresses basic issues regarding the derivation of the functional RG equation, taking as a starting point the functional integral on phase space rather than the functional integral over configuration space. The reason for listing it here is that the most striking consequence of this approach would be a quadratic rather than quartic running of the vacuum energy. In addition, the "reconstruction problem" of the bare action is addressed.

Dario Benedetti and Simone Speziale (2011)

Perturbative quantum gravity with the Immirzi parameter.
JHEP 1106, 107 (2011)

arXiv:1104.4028 [hep-th]


This paper uses standard perturbative methods to study the renormalization of gravity in first order formulation. In addition to Newton's constant, special attention is given to the behavior of the Immirzi parameter. In pure gravity the beta functions of these couplings lead to the familiar fixed point for Newton's constant, while the Immirzi parameter has fixed points at zero and infinity (in agreement with Daum and Reuter 2010). In the presence of fermions, torsion becomes dynamical and induces effective four fermion interactions. As expected, in the presence of fermions there are divergences that cannot be absorbed by a redefinition of the couplings. Still, one can define a flow of the Immirzi parameter and within the one loop approximation it is found that zero and infinity are not stable under renormalization; the Immirzi parameter flows instead to one in the UV.


Astrid Eichhorn, Holger Gies (2011)

Light fermions in quantum gravity.
New J. of Phys. 13, 125012 (2011)

arXiv:1104.5366 [hep-th]


Gravity is weak at low energy and strong near the Planck scale. Because it is universally attractive, one may suppose that it facilitates the formation of condensates. Then one may fear that in a fermionic system coupled to gravity a condensate forms, breaking chiral symmetry and giving a Planck-size mass to all fermions. In this paper the effect of gravity on four-fermion interactions is calculated, showing that this is not the case. Strong gravity seems therefore to be compatible with the existence of light fermions. This is good news for the asymptotic safety scenario, where the strength of gravity remains bounded but is nevertheless strong, but the results are useful also if the metric was only good as an effective field theory description, since the condition of the existence of light fermions can be used to put bounds on the regions of parameter space that are allowed phenomenologically.


Dario Benedetti (2011)

Asymptotic safety goes on shell
New J. of Phys. 14, 015005 (2012)

arXiv:1107.3110 [hep-th]


This article is devoted to an analysis of the gauge parameter dependence of the beta functions. By means of various technical improvements, the author manages to separate the on shell part of the calculation in a clean way, showing that it is gauge-parameter independent to all orders in the cosmological constant, as expected.

Max Niedermaier (2011)

Can a nontrivial gravitational fixed point be identified in perturbation theory?

PoS CLAQG08 (2011) 005

Alessandro Codello (2011)

Large N quantum gravity
New J. of Phys. 14, 015009 (2012)

arXiv:1108.1908 [hep-th]

This paper contains a calculation of contributions of matter loops to the gravitational effective action, based on the integration of the functional RG equation. The effective action is expanded up to third order in curvature. At high energy the trajectory is chosen to approach the nontrivial fixed point. In the course of the flow nonlocal terms develop, that give corrections to the Newtonian potential at low energy. Cubic terms enter in the part of the action that generates the trace anomaly.

Astrid Eichhorn (2011)

Observable consequences of quantum gravity: can light fermions exist?
J. Phys. Conf. Ser. 360, 012057 (2012)

arXiv:1109.3784 [gr-qc]


Talk given at Loops'11, Madrid, to appear in J. of Phys. Conf Ser.

Martin Reuter and Frank Saueressig (2011)

Fractal space-times under the microscope: a renormalization group view of Monte Carlo data
JHEP 1112, 012 (2011)

arXiv:1110.5224 [hep-th]

A detailed study of the scale dependence of various fractal dimensions according to the results of truncated functional RG calculations. A quantitative comparison is made with the numerical output of 3-dimensional CDT. The results are in good agreement and confirm that current Monte Carlo simulations do not probe the Planck scale yet.

Roberto Percacci (2011a)

A short introduction to asymptotic safety.

arXiv:1110.6389 [hep-th]


In the proceedings of the conference "Time and matter" Budva, Montenegro, October 2010.

Roberto Percacci (2011b)

RG flow of Weyl-invariant dilaton gravity.
New J. of Phys. 13, 125013 (2011)

arXiv:1110.6758 [hep-th]


It is shown here that the RG flow can be constructed in such a way as to preserve Weyl invariance, when a dilaton is present.

Frank Saueressig, Kai Groh, Stefan Rechenberger and Omar Zanusso (2011)

Higher derivative gravity from the universal renormalization group machine
PoS EPS-HEP 2011 124 (2011)

arXiv:1111.1743 [hep-th]

This is another test run of the universal renormalization group machine, this time in the context of higher derivative gravity.

Kai Groh, Frank Saueressig and Omar Zanusso (2011)

Off-diagonal heat kernel expansion and its application to fields with differential constraints

arXiv:1112.4856 [math-ph]

Martin Reuter and Frank Saueressig (2012a)

Quantum Einstein Gravity

arXiv:1202.2274 [hep-th]

A review of the asymptotic safety program applied to QEG - the quantum theory of gravity based on the metric as a carrier field of the physical degrees of freedom. Recent results on fractal dimensions of spacetime are extensively reviewed.

Ulrich Harst and Martin Reuter (2012)

The "tetrad only" theory space: nonperturbative renormalization flow and asymptotic safety
JHEP 1205 (2012) 005

arXiv:1203.2158 [hep-th]

Harst and Reuter study the RG flow of pure gravity in the Einstein-Hilbert truncation but using the tetrad rather than the metric as a fundamental variable. This differs from the calculation based on the metric in two ways. First, since the fluctuation of the metric contains terms that are quadratic in the fluctuation of the tetrad, the Hessian in the tetrad formalism contains terms that are proportional to the equation of motion and are not present in the metric formalism. Therefore, the two theories differ off shell. Second, the authors argue that the Lorentz ghosts (which have a purely algebraic ghost operator and are therefore usually discarded) do contribute to the running of the couplings. The results depend quite strongly on a parameter mu that has to be introduced in the ghost sector, and the results resemble those of the metric formulation only for mu in a small range near one. In particular the fixed point becomes UV repulsive for large mu and a limit cycle appears.

Ivan Donkin and Jan Pawlowski (2012)

The phase diagram of quantum gravity from diffeomorphism invariant RG flows

arXiv:1203.4207 [hep-th]

Calculation of the RG flow for gravity in a bimetric truncation that contains the Hilbert action for the background and terms linear and quadratic in the fluctuation, and using the Vilkovisky-de Witt geometrical formalism. The Nielsen identities are used to evaluate the difference between the background propagator and the fluctiation propagator. It is argued that there is a finite flow on the singular line leading to the point (1/2,0), which is therefore an IR attractive fixed point.

Astrid Eichhorn (2012)

Quantum gravity-induced matter self-interactions in the asymptotic safety scenario
Phys. Rev. D86, 105021 (2012)

arXiv:1204.0965 [hep-th]


Gravitational loops induce matter self-couplings even when none are present in the bare action. In this paper the case is studied of a single scalar with quartic derivative interactions. The beta functions of the scalar self-coupling and of Newton's constant, as well as the scalar anomalous dimension, are derived and found to admit two nontrivial fixed points.

S. Nagy, J. Krizsan and K. Sailer (2012)

Infrared fixed point in quantum Einstein gravity
JHEP 1207 (2012) 102

arXiv:1203.6564 [hep-th]


Dario Benedetti and Francesco Caravelli (2012)

The local potential approximation in quantum gravity
JHEP 1206 (2012) 017, Erratum-ibid. 1210 (2012) 157

arXiv:1204.3541 [hep-th]


It is argued that the f(R) truncation is the gravitational analog of the LPA for scalar theory. A new beta functional is derived for the function f and there is a discussion of issues that arise when one tries to find a solution for it. It is also argued that if such a solution exist the corresponding effective action must be simply R^2.

Nobuyoshi Ohta (2012)

Beta function and asymptotic safety in three dimensional higher derivative gravity
Class.Quant.Grav. 29 (2012) 205012

arXiv:1205.0476 [hep-th]

Using spectral sums on a three-sphere, the beta functions of the cosmological constant and Newton's constant are calculated. The action contains also generic higher derivative terms, whose beta functions are not given however.

Daniel Becker and Martin Reuter (2012)

Running boundary actions, asymptotic safety and black hole thermodynamics
JHEP 1207 (2012) 172

arXiv:1205.3583 [hep-th]

On a manifold with boundary a well posed variational problems requires the presence of a boundary term in the action, with  a specific coefficient. One can define two different "Newton's constants" as the coefficients of bulk and boundary terms. The RG flow of these couplings is studied in this paper, in two cases: the "single metric" Einstein-Hilbert truncation and a "bimetric" truncation containing terms linear in the metric fluctuation field. The latter truncation contains 17 flowing parameters and the running is induced by quantum fluctuations of a scalar field. It is found that the flow of the bulk and boundary Newton's constants does not preserve their ratio. Some remarks are made on role of the on-shell effective action as a device counting the number of field modes that are integrated out along the flow, in the spirit of Zamolodchokov's c-function. Consequences for black hole thermodynamics are pointed out.

Daniel Litim and Alejandro Satz (2012)

Limit cycles and quantum gravity

arXiv:1205.4218 [hep-th]

This paper contains a comparison of the RG flows in three models of quantum gravity. In order of increased complication, a minisuperspace model where the conformal factor depends only on time, conformally reduced gravity where the conformal factor is a general function of spacetime, and Einstein-Hilbert gravity. It is found that the first model contains an IR-attractive limit cycle, which disappears in the others. One can interpolate between the first two cases by treating the dimension in which the conformal factor fluctuates as a continuous parameter.

Martin Reuter and Frank Saueressig (2012b)

Asymptotic safety, fractals and cosmology

arXiv:1205.5431 [hep-th]

Lectures given at the Sixth Aegean Summer School on Quantum Gravity and Quantum Cosmology, Naxos, Greece, september 2011.

Stefan Rechenberger and Frank Saueressig (2012)

The R^2 phase diagram of QEG and its spectral dimension
Phys.Rev. D86 (2012) 024018
arXiv:1206.0657 [hep-th]

This paper analyzes in more detail the beta functions of gravity with an R^2 term, previously discussed in Lauscher and Reuter 2002b. Both in three and four dimensions, the beta functions have a singular locus that passes through the Gaussian fixed point.  This causes the properties of the flow around this point to depend on the limit in which the couplings are sent to zero. No trajectory is found that joins the non-Gaussian to the Gaussian fixed point. Nevertheless, some trajectories are identified that have a long classical regime. The spectral dimension along these trajectories is calculated.

Alfio Bonanno and Filippo Guarnieri (2012)

Universality and symmetry breaking in conformally reduced quantum gravity

Phys. Rev. D 86, 105027 (2012)
arXiv:1206.6531 [hep-th]

The authors derive the proper-time flow equation for conformally reduced quantum gravity and then solve it in various cases and with different cutoff functions. With spherical topology, the running Newton coupling can be obtained from the term quadratic in the conformal factor (the resulting anomalous dimension is called eta_pot), while in the flat topology it can be read from the kinetic term of the conformal factor (the resulting anomalous dimension is called eta_kin). The flow exhibits limit cycles. In order to study the flow of the potential of the conformal factor, a change of variables is introduced, which makes the equation linear in the second derivative. Some solutions are found: they develop a nontrivial minimum in the IR limit, which is interpreted as a phase of spontaneously broken diffeomorphism invariance. At large field the potential behaves like an inverse power of the conformal factor, suggesting the appearance of functions of the volume in the gravitational effective action.

Andreas Nink and Martin Reuter (2012)

On the physical mechanism underlying asymptotic safety
JHEP 1301 (2013) 062

arXiv:1208.0031 [hep-th]

The preceding literature provides many calculations supporting the existence of a gravitational fixed point but do not shed much light on the physical mechanism underlying asymptotic safety. This paper fills this gap by providing heuristic arguments for gravitational antiscreening. The discussion follows closely known arguments for QED and Yang--Mills theory, whose beta functions are dominated by "paramagnetic" terms. Also in the case of gravity, the interaction of the graviton fluctuation with the gravitational background can be split into "diamagnetic" and "paramagnetic" terms, which contribute with opposite signs to the beta functions. In d>3 the latter dominate and are responsible for antiscreening. It is also shown, in a weak field approximation where gravitational effects can be split into "electric" and "magnetic" ones, that the gravitational vacuum behaves as a paramagnetic medium.

Maximilian Demmel, Frank Saueressig and Omar Zanusso (2012)

Fixed-functionals of three-dimensional Quantum Einstein Gravity
JHEP 1211 (2012) 131
arXiv:1208.2038 [hep-th]

The problem addressed by Benedetti and Caravelli (2012) is treated here in the simplified context of conformally reduced gravity in three dimensions. In this case numerical solutions can be found.

Nicolai Christiansen, Daniel Litim, Jan Pawlowski and Andreas Rodigast (2012)

Fixed points and infrared completion of quantum gravity
Phys.Lett. B728 (2014) 114-117

arXiv:1209.4038 [hep-th]

Most of the previous work on gravitational beta functions has been done by following the flow of the coefficients of the background effective action. This paper presents an alternative calculation in flat space where the beta functions are derived from the graviton inverse propagator, and precisely the beta function of Newton's constant is read from the momentum squared term and that of the cosmological constant from the momentum-independent term. For this paper it is crucial that the coefficient of the momentum-squared term is read from a Taylor expansion around momentum of order of the cutoff. These beta functions lead to a flow that resembles the usual one near the Gaussian and non-Gaussian fixed points, but in addition has a smooth behavior near Lambda=1/2, which now appears as an IR fixed point.

Roberto Percacci and Pietro Dona' (2012)

Functional renormalization with fermions and tetrads
Phys.Rev. D87 (2013) 045002
arXiv:1209.3649 [hep-th]


This paper addresses two issues that arise when gravity is coupled to fermions: the first is the sign of the fermionic contribution to the running of Newton's constant, the second is the difference between the gravitational beta functions in metric and tetrad formalism. It is common practice to compute the one loop fermionic effective action as one half the trace of the logarithm of the square of the Dirac operator. When a cutoff is imposed on the square of the Dirac operator, the sign of the beta functions differs when one uses a cutoff that depends on -Box (type I) or on the square of the Dirac operator -Box+R/4 (type II). To decide which one of these gives the right result, the beta function is computed using a spectral sum, with the cutoff imposed directly on the Dirac operator (rather than its square). This agrees with the type II cutoff. Arguments are then given for why the type I cutoff should have been avoided in the first place.
The gravitational beta functions had been worked out in tetrad formalism by Harst and Reuter (2012). Here the analysis is extended by considering more general cutoff types (type I or II, with or without using the York decomposition), and with a gauge parameter. It appears that when the York decomposition is used the results are much less sensitive to mu, and resemble those of the metric formalism even for mu tending to infinity (which corresponds to dropping the Lorentz ghost contribution). Pathologies reappear when the gauge parameter becomes of order two.

Astrid Eichhorn (2012)

Experimentally testing asymptotically safe quantum gravity with photon-photon scattering

arXiv:1210.1528 [hep-th]


Talk given at the 13th Marcel Grossmann meeting (Stockholm, july 2013)

Alessandro Codello, Giulio d'Odorico, Carlo Pagani and Roberto Percacci (2012)

Renormalization group and Weyl invariance.
Class.Quant.Grav. 30 (2013) 115015

arXiv:1210.3284 [hep-th]


The main result of this paper is a general proof that when one quantizes a classically Weyl invariant system in the presence of a dilaton, one can construct an effective action that is also Weyl invariant. This is proven by constructing a flow that is Weyl invariant. The construction is given first for non-interacting matter coupled to external gravity and then extended to interacting matter and dynamical gravity. Even though Weyl invariance remains unbroken, the trace anomaly is present as usual. Some explicit calculations of Weyl-invariant effective actions are given in two and four dimensions. Various issues are addressed, such as the meaning of a cutoff in a conformal theory, or the notion of flow in a space of conformal theories.

S. Nagy (2012)

Lectures on renormalization and asymptotic safety
Ann. Phys. (2013) 310-346

arXiv:1211.4151 [hep-th]

Juergen A. Dietz and Tim R. Morris (2012)

Asymptotic safety in the f(R) approximation
JHEP 1301 (2013) 108
arXiv:1211.0955 [hep-th]

This paper makes important progress in the analysis of the exact RG equation for gravity in the truncation where the effective average action is truncated to a function of the scalar curvature. It analyzes the equation for f(R) written by Benedetti and Caravelli (2012). Arguments are given to the effect that the number of solutions of the fixed point equation can be reliably determined by parameter counting. Given that the equation is third order, one would need to provide three conditions to reduce the number of solutions to a discrete set. Two such conditions are provided by the requirement that the solution continues past the two singularities of the equation for positive R. Accordingly, several lines of fixed points are identified. Such fixed points would lead to a continuum of eigen-perturbations, a physically unacceptable situation. It is suggested that the correct solutions must be valid also for negative R, where a further singularity in the equation provides an additional restriction. Numerical analyses support these conclusions, but a solution extending from minus to plus infinity is not found.

Daniel Becker and Martin Reuter (2012)

Asymptotic safety and black hole thermodynamics

arXiv:1212.4274 [hep-th]

In the proceedings of the XIII Marcel Grossmann Meeting

Andreas Nink and Martin Reuter (2012)

On quantum gravity, asymptotic safety and paramagnetic dominance

arXiv:1212.4325 [hep-th]

To appear in the proceedings of the XIII Marcel Grossmann Meeting

Astrid Eichhorn (2013b)

On unimodular quantum gravity
Class.Quant.Grav. 30 (2013) 115016

arXiv:1301.0632 [hep-th]

A calculation of the beta function of Newton's constant in unimodular gravity.

Astrid Eichhorn (2013a)

Faddeev-Popov ghosts in quantum gravity beyond perturbation theory

Class. and Quantum Grav. 30, 115016 (2013)

arXiv:1301.0879 [hep-th]

Stefan Rechenberger and Frank Saueressig (2012)

A functional renormalization group equation for foliated spacetimes
JHEP 1303 (2013) 010

arXiv:1212.5114 [hep-th]

Dario Benedetti (2013)

On the number of relevant operators in asymptotically safe gravity

Europhys.Lett. 102 (2013) 20007

arXiv:1301.4422 [hep-th]


Based on the general properties of the flow equation for f(R) (in a slightly different form from the one of Benedetti and Caravelli 2012) it is shown that if a scaling solution exists, it must have a finite number of relevant perturbations.

K. Falls, D. Litim, K. Nikolakopulos and C. Rahmede (2013)

A bootstrap towards asymptotic safety

arXiv:1301.4191 [hep-th]

The flow of f(R) gravity is explored using improved techniques for polynomials up to order 34, confirming and extending previous results. The scaling exponents exhibit a structure that is relatively close to Gaussian behavior.

Jan-Eric Daum, Martin Reuter (2013)

Einstein-Cartan gravity, asymptotic safety and the running Immirzi parameter

Annals Phys. 334 (2013) 351-419

arXiv:1301.5135 [hep-th]


A detailed account of the calculations in Daum and Reuter (2010a).

R. Percacci, C. Pope, M. Perry and E. Sezgin (2013)

Beta functions of topologically massive supergravity

JHEP 1403 (2014) 083

arXiv:1302.0868 [hep-th]


Extends previous paper by Percacci and Sezgin to include fermionic contributions. Calculations are done both on the sphere (positive cosmological constant) and hyperboloid (negative cosmological constant).

Alfio Bonanno, Martin Reuter (2013)

Modulated ground state of gravity theories with stabilized conformal factor.
Phys. Rev. D.87, 084019

arXiv:1302.2928 [hep-th]

It is shown that in conformally reduced version of R+R^2 theory the ground state breaks translation invariance and corresponds to a periodic wave. This may provide an answer to the issue of the instability of the conformal factor.

Alessandro Codello, Giulio d'Odorico, Carlo Pagani (2013)

Consistent closure of RG flow equations in quantum gravity

Phys.Rev. D89 (2014) 081701

arXiv:1304.4777 [gr-qc]


In this paper the anomalous dimension of the graviton and ghost are calculated from the respective two-point functions. When the result is inserted in the flow equations for the Einstein-Hilbert truncation a nontrivial fixed point is found, with very small and negative cosmological constant, and real scaling exponents.

G. Calcagni, A. Eichhorn and F. Saueressig (2013)

Probing the quantum nature of spacetime by diffusion
Phys.Rev. D87 (2013) 12, 124028

arXiv:1304.7247 [hep-th]

Juergen A. Dietz and Tim R. Morris (2013)

Redundant operators in the exact renormalisation group and in the f(R) approximation to asymptotic safety
JHEP 1307 (2013) 064

arXiv:1306.1223 [hep-th]

Nobuyoshi Ohta and Roberto Percacci (2013)

Higher derivative gravity and asymptotic safety in diverse dimensions

Class.Quant.Grav. 31 (2014) 015024

arXiv:1308.3398 [hep-th]


Revisits the calculation of the beta functions in higher derivative gravity. The main new result is the extension to dimensions different than four. The cases three, five and six are discussed in some detail. Due to differences in the heat kernel coefficients, the results do not agree with previous calculations of de Berredo Peixoto and Shapiro in 4+epsilon dimensions.

Dario Benedetti and Filippo Guarnieri (2013)

Brans-Dicke theory in the local potential approximation

New J.Phys. 16 (2014) 053051

arXiv:1311.1081 [hep-th]


This is a study of the flow equations for the scalar potential in Brans-Dicke-theory, motivated in part by the classical equivalence of the f(R) theory and scalar-tensor theory. Only the case when the Brans-Dicke parameter is equal to zero is studied in detail. The fixed point equation for the potential is derived in two different gauges and solutions are found to be very different in the two cases. The inconsistency is attributed to the restriction on the Brans-Dicke parameter.

Pietro Dona', Astrid Eichhorn and Roberto Percacci (2013)

Matter matters in asymptotically safe quantum gravity
Phys.Rev. D89 (2014) 084035

arXiv:1311.2898 [hep-th]


As in QCD too many fermions spoil asymptotic freedom, it is conceivable that in quantum gravity too many matter fields could spoil asymptotic safety. This issue is addressed under the following approximations: the Einstein-Hilbert truncation for gravity but retaining a nontrivial wave function renormalization for the graviton and ghost; minimal coupling for matter, neglecting all self interactions but keeping track of the wave function renormalization. The main novelty are the matter contribution to the gravitational anomalous dimension and the gravitational contribution to the matter anomalous dimension. For a given number of gauge fields there is a finite number of allowed combinations of scalar and fermion fields.

Carlo Pagani and Roberto Percacci (2013)

Quantization and fixed points of non-integrable Weyl theory
Class. Quant. Grav. 31 (2014) 115005

arXiv:1312.7767 [hep-th]


Complementing earlier results on integrable Weyl theory, here the RG flow is derived for a Weyl invariant theory containing the metric, a scalar field and Weyl's gauge field. Special attention is payed to the relation between the cases when the scalar is massive and massless.

Maximilian Demmel, Stefan Rechenberger and Omar Zanusso (2014)

RG flows of Quantum Einstein Gravity on maximally symmetric spaces
JHEP 1406 (2014) 026

arXiv:1401.5495 [hep-th]

A study of the flow equation for conformally reduced f(R) gravity in three dimensions. Two scaling solutions are found.

Nicolai Christiansen, Jan Pawlowski and Andreas Rodigast (2014)

Global flows in quantum gravity
Phys.Rev. D93 (2016) no.4, 044036

arXiv:1403.1232 [hep-th]

Daniel Becker and Martin Reuter (2014a)

En route to background independence: broken split-symmetry and how to restore it with bi-metric average actions.
Annals Phys. 350 (2014) 225-301

arXiv:1404.4537 [hep-th]

A detailed analysis of bimetric gravity with Einstein-Hilbert action both for the full and background metric. The truncation involves four couplings: dynamical and background cosmological constant, dynamical and background Newton constant. (These can be also reparametrized as level zero and level one cosmological constant and Newton constant.) The flow equations of the dynamical couplings form a closed subsystem admitting three fixed points: a Gaussian one and two non-Gaussian ones, of which one has negative couplings. The flow of the background couplings depends on the solution one chooses for the dynamical ones and is therefore non-autonomous. One can nevertheless describe complete, asymptotically safe trajectories from the UV to the IR. These trajectories chase a moving attractor. The flow around the fixed point in the dynamical subsector follows spirals while the flow in the background subsector has real critical exponents. There are four relevant directions. Nevertheless the requirement of restoration of split symmetry in the IR selects a two-parameter family of trajectories.

Daniel Becker and Martin Reuter (2014b)

Propagating gravitons vs. dark matter in asymptotically safe quantum gravity
JHEP 1412 (2014) 025

arXiv:1407.5848 [hep-th]

This paper is dedicated to the issue of the sign of the anomalous dimension. In single-metric truncations the anomalous dimension is obtained directly from the beta function of Newton's constant and must be equal to -2 at a fixed point. This is incompatible with a Källen-Lehmann representation of the two point function.
Using the results of the double-Einstein-Hilbert truncations studied in Manrique, Reuter, Saueressig (2010b) and Becker and Reuter (2014a) it is shown that when the
("dynamical" or "level one") cosmological constant is below a certain positive value, and in particular near the Gaussian fixed point, the ("dynamical" or "level one") anomalous dimension is positive, and hence compatible with the Källen-Lehmann representation and with the notion of propagating gravitons.
Some speculations on possible astrophysical consequences are put forward.

Kevin Falls (2014)

Asymptotic safety and the cosmological constant
JHEP 1601 (2016) 069

arXiv:1408.0276 [hep-ph]


This paper revisits the Einstein-Hilbert truncation with some improvements. As in Benedetti (2011) care is taken to separate the effect of the physical modes from the gauge degrees of freedom, and to isolate the terms that vanish on shell. A type III cutoff is used but unlike Codello, Percacci, Rahmede (2009), where infinitely many heat kernel coefficients were resummed, here only the first two terms of the heat kernel expansion are retained. With these choices, the phase portrait is studied and the critical exponents at the non-Gaussian fixed point are found to be real. (Previously real critical exponents had only been found in bimetric truncations). The conformal reduction is studied by keeping the conformal factor and a scalar ghost that cancels its contribution on shell, so as to have a topological field theory. In this reduced theory the critical exponent is 1/3 with suitable choices of cutoff, reproducing lattice results by Hamber.

Pietro Dona', Astrid Eichhorn and Roberto Percacci (2014)

Consistency of matter models with asymptotically safe quanum gravity
Canadian Journal of Physics, 2015, 93(9): 988-994

arXiv:1410.4411 [hep-th]

Proceedings of Theory Canada 9.

K. Falls, D. Litim, K. Nikolakopulos and C. Rahmede (2013)

Further evidence for asymptotic safety of quantum gravity
Phys.Rev. D93 (2016) no.10, 104022

arXiv:1410.4815 [hep-th]

Much more detail of the calculations originally reported in Falls et al. 2013.

Ippocratis Saltas (2014)

On the UV structure of quantum unimodular gravity

arXiv:1410.6163 [hep-th]

Andreas Nink

Field parametrization dependence in asymptotically safe quantum gravity
Phys.Rev. D91 (2015) 4, 044030

arXiv:1410.7816 [hep-th]

This paper contains a discussion of the use of the exponential parametrization for the metric. It revisits the results for the fixed points in 2+epsilon dimensions, and then in four dimensions, both in single-metric truncation and in bimetric truncation (following Becker and Reuter 2014a).

Ulrich Harst and Martin Reuter (2014)

A new functional flow equation for Einstein-Cartan quantum gravity
Annals Phys. 354 (2015) 637-704

arXiv:1410.7993 [hep-th]

In order to ease the technical difficulties encountered in the application of the ERGE to Einstein-Cartan theory (Daum and Reuter) this paper develops and then uses a "special purpose" simplified functional equation
. As in previous papers, only the cosmological constant, Newton's constant and Immirzi parameter are taken into account. Since not all terms of the same order in derivatives are considered, reading off the beta functions of the couplings presents ambiguities, which are illustrated by choosing different parametrizations of the action. Common features and differences between this and earlier treatments are pointed out.

Daniel Becker and Martin Reuter (2014c)

Towards a C-function in quantum gravity
JHEP 1503 (2015) 065

arXiv:1412.0468 [hep-th]

The on-shell effective average action is proposed as a mode-counting function. Its working is illustrated in the Einstein-Hilbert truncation, where it is monotonic in the bimetric truncation but not in the single-metric treatment.

Alessandro Codello, Giulio d'Odorico (2014)

Scaling and renormalization in two-dimensional quantum gravity
Phys.Rev. D92 (2015) 2, 024026

arXiv:1412.6837 [gr-qc]


The first part of this paper contains a review of known scaling relations of two-dimensional quantum gravity. In the second part the scaling exponents are calculated using the functional RG, both in 2 dimensions (where the flow is driven by the Polyakov action) and 2+epsilon dimensions (where it is driven by the Hilbert term). The known correct result of the central charge -25 is only reproduced if one uses the exponential parametrization.

Maximilian Demmel, Frank Saueressig and Omar Zanusso (2014)

RG flows of Quantum Einstein Gravity in the linear-geometric approximation

Annals Phys. 359 (2015) 141-165
arXiv:1412.7207 [hep-th]

The Wetterich equation for f(R) gravity is written in a gauge where only physical degrees of freedom are retained. It is shown that in d=4 polynomial truncations admit a fixed point that has similar properties to the well-known one.

Roberto Percacci and Gian Paolo Vacca (2015a)

Search of scaling solutions in scalar-tensor gravity
Eur.Phys.J. C75 (2015) 5, 188
arXiv:1501.00888 [hep-th]


The flow equation for a scalar-tensor theory of type V-FR is written using the exponential parametrization of the metric and a "physical unimodular" gauge, where the trace and spin one components of the metric fluctuation are put to zero. In this gauge there is no undifferentiated potential appearing in the hessian, so that the flow is free of IR singularities. The resulting flow equations are much simpler than those of Narain and Percacci (2009b). Besides the "Gaussian matter fixed point" with constant V and F, there is, in any dimension d>2, a nontrivial solution with constant V and quadratic F. In d=3 there is evidence for an analog of the Wilson-Fisher fixed point, but no proof of global existence is given.

Kevin Falls (2015)

On the renormalization of Newton's constant
Phys.Rev. D92 (2015) no.12, 124057

arXiv:1501.05331 [hep-th]


It is shown that for the Einstein-Hilbert truncation there exists a parametrization of the gravitational degrees of freedom that makes the beta functions independent of gauge parameters.

Astrid Eichhorn (2015)

The renormalization group flow of unimodular f(R) gravity
JHEP 1504 (2015) 096

arXiv:1501.05848 [hep-th]

The flow equation for the function f is calculated in unimodular gravity, using spectral sums. Approximate polynomial solutions are discussed.

Julia Borchardt and Benjamin Knorr (2015)

Global solutions of functional fixed point equations via pseudo-spectral methods
Phys.Rev. D91 (2015) 10, 105011
arXiv:1502.07511 [hep-th]


The paper illustrates the use of Chebyshev polynomial in the solution of functional fixed point equations. It gives a complete solution for the equations of arXiv:1501.00888 [hep-th], in three dimensions.

Daniel Becker and Martin Reuter (2015)

Is there a C-function in 4d quantum Einstein Gravity

arXiv:1502.03292 [hep-th]

Talk given by Martin Reuter at Quantum Mathematical Physics, Regensburg 2014

Juergen A. Dietz and Tim R. Morris (2015)

Background-independent exact renormalization group for conformally reduced gravity
JHEP 1504 (2015) 118

arXiv:1502.07396 [hep-th]

The flow equation for conformally reduced gravity is supplemented by the "split symmetry Ward identity" to construct a background-independent flow equation. The notion of fixed point in this context is discussed. The parametrization of the conformal d.o.f. is kept arbitrary.

Maximilian Demmel, Frank Saueressig and Omar Zanusso (2015)

A proper fixed functional for four-dimensional Quantum Einstein Gravity
JHEP 1508 (2015) 113

arXiv:1504.07656 [hep-th]

A family of flow equation for f(R) gravity are given, depending on numerical parameters that define the operators used to define the r.h.s of the flow equation. The parameters are fixed based on some criteria, in particular that the number of fixed singularitues matches the order of the equation. Then, a complete (0<R<infinity) fixed point solution for a flow equation is found.

Peter Labus, Roberto Percacci and Gian Paolo Vacca (2015)

Asymptotic safety in O(N) scalar models coupled to gravity
Phys.Lett. B753 (2016) 274-281
arXiv:1505.05393 [hep-th]


The results of Percacci and Vacca (2015) are generalized to the case of an N-plet of scalar fields. For N>2 there is an additional solution in closed form.

Andreas Nink and Max Demmel (2015)

Connections and geodesics in the space of metrics
Phys.Rev. D92 (2015) no.10, 104013

arXiv:1506.03809 [gr-qc]

Nicolai Christiansen, Benjamin Knorr, Jan Meibohm, Jan Pawlowski and M. Reichert (2015)

Local quantum gravity
Phys.Rev. D92 (2015) no.12, 121501

arXiv:1506.07016 [hep-th]

The running Newton constant is derived from the graviton three point function.

Nobuyoshi Ohta, Roberto Percacci and Gian Paolo Vacca (2015a)

Flow equation for f(R) gravity and some of its exact solutions
Phys. Rev. D92 (2015) 6, 061501
arXiv:1507.00968 [hep-th]


The flow equation for f(R) gravity is written in exponential parametrization and physical gauge. As in Demmel, Saueressig and Zanusso, the cutoff depends on some parameters, the coefficients of the endomorphism in the operator used to construct the cutoff. There are discrete choices of the parameters for which the equation admits a quadratic solution. When the parameters change continuously, the solution seems also to change continuously, at least in polynomial truncation.

Tim R. Morris and Zoe H. Slade (2015)

Solutions to the reconstruction problem in asymptotic safety
JHEP 1511 (2015) 094
arXiv:1507.08657 [hep-th]

Holger Gies, Benjamin Knorr and  Stefan Lippoldt (2015)

Generalized Parametrization Dependence in Quantum Gravity
Phys.Rev. D92 (2015) no.8, 084020

arXiv:1507.08859 [hep-th]


The product G*Lambda and the scaling exponent are computed both in linear and exponential parametrization, and their gauge dependence is studied, with the aim of identifying the most reliable parametrization.

Martin Reuter and Gregor M. Schollmeyer (2015)

The metric on field space, functional renormalization and metric-torsion quantum gravity
Ann. Phys. (2016)

arXiv:1509.05041 [hep-th]

Kin-ya Oda and Masatoshi Yamada (2016)

Non-minimal coupling in Higgs–Yukawa model with asymptotically safe gravity
Class.Quant.Grav. 33 (2016) no.12, 125011

arXiv:1510.03734 [hep-th]

An extension of the work of Narain and Percacci (2009b) including the effect of fermions with Yukawa couplings.

Jan Meibohm, Jan Pawlowski and M. Reichert (2015)

Asymptotic safety of gravity-matter systems
Phys.Rev. D93 (2016) no.8, 084035

arXiv:1510.07018 [hep-th]

The authors study the effect of scalars and fermions on the fixed point of the "level-three" Newton constant.

Ulrich Harst and Martin Reuter (2015)

On selfdual spin-connections and Asymptotic Safety
Phys.Lett. B753 (2016) 395-400

arXiv:1509.09122 [hep-th]

Dario Benedetti (2015)

Essential nature of Newton's constant in unimodular gravity
Gen.Rel.Grav. 48 (2016) no.5, 68
arXiv:1511.06560 [hep-th]

Nobuyoshi Ohta, Roberto Percacci and Gian Paolo Vacca (2015a)

Renormalization Group Equation and scaling solutions for f(R) gravity in exponential parametrization
European Physical Journal C (2016) 76:46
arXiv:1511.09393 [hep-th]


More details are given of the solutions found in the preceding paper. In addition, numerical solutions are studied for selected values of the endomorphism parameters.

Andreas Nink and Martin Reuter (2015)

The unitary conformal field theory behind 2D asymptotic safety
JHEP 1602 (2016) 167


Pietro Dona', Astrid Eichhorn, Peter Labus and Roberto Percacci (2015)

Asymptotic safety in an interacting system of gravity and scalar matter
Phys.Rev. D93 (2016) no.4, 044049

arXiv:1512.01589 [hep-th]

The running Newton constant is derived from the graviton-scalar three point function.

Alfio Bonanno and Alessia Platania (2015)

Asymptotically safe R+R^2 Gravity

Holger Gies, Benjamin Knorr, Stefan Lippoldt and Frank Saueressig (2016)

The Gravitational Two-Loop Counterterm is Asymptotically Safe
Phys.Rev.Lett. 116 (2016) no.21, 211302

arXiv:1601.01800 [hep-th]

The fixed point if studied in the truncation containing the Hilbert action and the Weyl-cube term that appears as a perturbative counterterm at two loops.

Jan Meibohm, Jan Pawlowski (2016)

Chiral fermions in asymptotically safe quantum gravity
Eur.Phys.J. C76 (2016) no.5, 285

arXiv:1601.04597 [hep-th]

A study of the issue of chiral symmetry breaking, or lack thereof, due to the gravitational interactions.

Tim R. Morris and Anthony W.H. Preston (2016)

Manifestly diffeomorphism invariant classical Exact Renormalization Group
JHEP 1606 (2016) 012
arXiv:1602.08993 [hep-th]

Peter Labus, Tim R. Morris and Zoe H. Slade (2016)

Background independence in a background dependent renormalization group
Phys.Rev. D94 (2016) no.2, 024007
arXiv:1603.04772 [hep-th]

Astrid Eichhorn, Aaron Held and Jan Pawlowski (2016)

Quantum gravity effects on a Higgs-Yukawa model
Phys.Rev. D94 (2016) no.10, 104027
arXiv:1604.02041 [hep-th]

Nobuyoshi Ohta, Roberto Percacci and Antonio Duarte Pereira (2016a)

Gauges and functional measures in quantum gravity I: Einstein theory
JHEP 1606 (2016) 115 
arXiv:1505.00454 [hep-th]


This paper contains a general computation of the off-shell one-loop divergences in Einstein gravity on the sphere, using a two-parameter family of path integral measures, corresponding to different ways of parametrizing the graviton field, and a two-parameter family of gauges. Trying to reduce the gauge- and measure-dependence selects certain classes of measures and gauges respectively. There is a choice of two parameters (corresponding to the exponential parametrization and the partial gauge condition that the quantum field be traceless) that automatically eliminates the dependence on the remaining two parameters and on the cosmological constant. It is observed that the divergences are invariant under a Z_2 "duality" transformation that (in a particularly important special case) involves the replacement of the densitized metric by a densitized inverse metric as the fundamental quantum variable. This singles out a formulation of unimodular gravity as the unique "self-dual" theory in this class.

Tobias Henz, Jan Pawlowski and Christoph Wetterich (2016)

Scaling solutions for Dilaton Quantum Gravity
Phys.Lett. B769 (2017) 105-110

arXiv:1605.01858 [hep-th]

Jurgen Dietz, Tim R. Morris and Zoe H. Slade (2016)

Fixed point structure of the conformal factor field in quantum gravity
Phys.Rev. D94 (2016) no.12, 124014
arXiv:1605.07636 [hep-th]

Nobuyoshi Ohta and Kevin Falls (2016)

Renormalization Group Equation for f(R) gravity on hyperbolic spaces
Phys.Rev. D94 (2016) no.8, 084005  
arXiv:1507.08460 [hep-th]


This paper extends previous work of Ohta et al from the case of compact to non-compact background. It is found that the polynomial expansion does not yield stable result as the truncation is extended.

Jorn Biemans, Alessia Platania and Frank Saueressig (2016)

Quantum gravity on foliated spacetime - asymptotically safe and sound
Phys.Rev. D95 (2017) no.8, 086013

arXiv:1609.04813 [hep-th]

Tim R. Morris (2016)

Large curvature and background scale independence in single-metric approximations to asymptotic safety
JHEP 1611 (2016) 160
arXiv:1610.03081 [hep-th]

Recall that any classical gravitational action is invariant under any infinitesimal change of the background, provided the fluctuation is changed by the opposite amount (in the ordinary linear parametrization). This paper focuses just on constant rescalings of the background. The Ward identity for such transformations contains many pieces that in general prevent one from solving it simultaneously with the flow equation. This is an obstruction to obtaining a single-field flow. It is shown in this paper that in six dimensions the anomalous part of the Ward identity becomes identical to the r.h.s. of the flow equation. The two can then be solved with the method of characteristics to give a flow equation that depends on one less fluctuation degree of freedom.

Nobuyoshi Ohta, Roberto Percacci and Antonio Duarte Pereira (2016b)

Gauges and functional measures in quantum gravity II: higher derivative gravity
Eur.Phys.J. C77 (2017) no.9, 611
arXiv:1610.07991 [hep-th]


The analysis of OPP (2016a) is extended to the case when the action contains Ricci squared and Ricci scalar squared terms. The background is assumed to be Einstein. The York decomposition is used in conjunction with Lichnerowicz Laplacians. The results are very similar, in particular the duality is found also in this case.

Astrid Eichhorn and Stefan Lippoldt (2016)

Quantum gravity and standard model-like fermions
Phys.Lett. B767 (2017) 142-146

arXiv:1611.05878 [hep-th]

Carlo Pagani and Martin Reuter (2016)

Composite operators in asymptotic safety
Phys.Rev. D95 (2017) no.6, 066002
arXiv:1611.06522 [hep-th]

In view of calculating observables in an asymprotically safe theory of gravity, this paper derives formulae for the anomalous dimension of composite operators. Sample calculations are presented in conformally-reduced Einstein-Hilbert gravity and two-dimensional gravity.

Roberto Percacci and Gian Paolo Vacca (2016)
The background scale Ward identity in quantum gravity
Eur.Phys.J. C77 (2017) no.1, 52
arXiv:1611.07005 [hep-th]


This paper follows Morris (2016) but with three differences at the technical level: the exponential parametrization of the metric, a higher-derivative gauge fixing and a "pure" cutoff. It is shown that with these modifications the anomalous terms in the scale Ward identity (recall that the classical action is background scale invariant) is equal to the r.h.s. of the flow equation, in any dimension.

Nicolai Christiansen (2016)

Four-derivative quantum gravity beyond perturbation theory

arXiv:1612.06223 [hep-th]

This paper extends previous work on the vertex expansion to four-derivative gravity. The 3- and 4-point vertices are taken from the Hilbert action plus terms quadratic in Ricci scalar and Ricci tensor. The flow of the 2-point function is studied, in all its spin components. From it, the beta functions of three couplings and the anomalous dimension are read off. Newton's constant is either treated as an external parameter, or is obtained from the running of the three-point vertex. There is a fully non-perturbative fixed point with two attractive directions. The one-loop beta functions of the higher-derivative couplings obtained in this way do not agree with the standard perturbative calculations.

T. Denz, J. Pawlowski and M. Reichert (2016)

Towards apparent convergence in asymptotically safe quantum gravity
Eur.Phys.J. C78 (2018) no.4, 336

arXiv:1612.07315 [hep-th]

This paper contains a study of the vertex expansion up to the four-point function. Using a symmetric momentum configuration the 3- and 4-point vertices become functions of a single external momentum. The dependence on this momentum is studied, from zero up to the cutoff k. From this dependence the beta functions of zero- two- and four-derivative couplings can be read off by means of suitable definitions. The resulting flow has a fixed point with three attractive directions.

Nobuyoshi Ohta (2017)

Background scale independence in quantum gravity
PTEP 2017 (2017) no.3, 033E02
arXiv:1701.01506 [hep-th]

Kevin Falls (2017)

Physical renormalization schemes and asymptotic safety in quantum gravity
Phys.Rev. D96 (2017) no.12, 126016  

arXiv:1702.03577 [hep-th]

Jorn Biemans, Alessia Platania and Frank Saueressig (2017)

Renormalization group fixed points of foliated gravity-matter systems
JHEP 1705 (2017) 093

arXiv:1702.06539 [hep-th]

The fixed point of quantum gravity is studied in the ADM formalism on a FRW background, using a novel gauge fixing. The effect of matter fields is summarized in two effective parameters, and the dependence of the results on these parameters is studied.

Astrid Eichhorn and Nicolai Christiansen (2017)

An asymptotically safe solution to the U(1) triviality problem
Phys.Lett. B770 (2017) 154-160

arXiv:1702.07724 [hep-th]

The following three points are made. While asymptotic freedom of the standard gauge coupling is compatible with gravitational interactions, higher gauge couplings of the type (F^2)^2 are necessarily generated. Thus asymptotic safety of gravity implies that these couplings cannot be zero. Reality of this fixed point puts bounds on the strength of the gravitational coupling. Finally, these new couplings contribute to the running of the (asymptotically free) gauge coupling with opposite sign relative to the direct gravitational effect. They become dominant for sufficiently strong gravitational coupling, making the gauge coupling irrelevant. This would be hard to reconcile with observations. Using numbers from Dona', Eichhorn and Percacci, it seems that this does not happen, so that the gauge coupling remains relevant.

Yuta Hamada and Masatoshi Yamada (2017)

Asymptotic safety of higher derivative quantum gravity non-minimally coupled with a matter system
arXiv:1703.09033 [hep-th]

Sergio Gonzales-Martin, Tim R. Morris and Zoe H. Slade (2017)

Asymptotic solutions in asymptotic safety
Phys.Rev. D95 (2017) no.10, 106010
arXiv:1704.08873 [hep-th]


W.B. Houthoff, A. Kurov and Frank Saueressig (2017)

Impact of topology in foliated Quantum EInstein Gravity

arXiv:1705.01848 [hep-th]

Nicolai Christiansen, Astrid Eichhorn and Aaron Held (2017)

Is scale-invariance in gauge-Yukawa systems compatible with the graviton?
Phys.Rev. D96 (2017) no.8, 084021

arXiv:1705.01858 [hep-th]

Astrid Eichhorn and Aaron Held (2017)

Top mass from asymptotic safety
Phys.Lett. B777 (2018) 217-221

arXiv:1707.01107 [hep-th]

Benjamin Knorr and  Stefan Lippoldt (2017)

Correlation functions on a curved background

arXiv:1707.01397 [hep-th]

S. Nagy, B. Fazekas, Z. Peli, K. Sailer and I. Steib (2017)

Regulator-dependence of fixed points in quantum Einstein gravity with R^2 truncation

arXiv:1707.04934 [hep-th]

Carlos M. Nieto, Roberto Percacci and Vedran Skrinjar (2017)
Split Weyl transformations in quantum gravity
Phys.Rev. D96 (2017) no.10, 106019

arXiv:1708.09760 [hep-th]

Astrid Eichhorn (2017)

Status of the asymptotic safety paradigm for quantum gravity and matter
Found.Phys. 48 (2018) no.10, 1407-1429

arXiv:1709.03696 [hep-th]

Proceedings of the conference "Black holes, gravitational waves and spacetime singularities", Specola Vaticana, Rome, May 9-12, 2017

Astrid Eichhorn and Fleur Versteegen (2017)

Upper bound on the abelian gauge coupling from asymptotic safety
JHEP 1801 (2018) 030

arXiv:1709.07252 [hep-th]

Daniel Becker, Chris Ripken and Frank Saueressig (2017)

On avoiding Ostrogradski instabilities within asymptotic safety
JHEP 1712 (2017) 121

arXiv:1709.09098 [hep-th]

Alessia Platania and Frank Saueressig (2017)

Functional renormalization group flows on Friedmann-Lemaitre-Robertson-Walker backgrounds
Found.Phys. 48 (2018) no.10, 1291-1304

arXiv:1710.01972 [hep-th]

Proceedings of the conference "Black holes, gravitational waves and spacetime singularities", Specola Vaticana, Rome, May 9-12, 2017

Astrid Eichhorn, Stefan Lippoldt and Vedran Skrinjar (2017)

Nonminimal hints for asymptotic safety
Phys.Rev. D97 (2018) no.2, 026002

arXiv:1710.03005 [hep-th]

Nicolai Christiansen, Daniel F. Litim, Jan M. Pawlowski and Manuel Reichert (2017)

Asymptotic safety of gravity with matter
(Formerly" One force to rule them all: asymptotic safety of gravity with matter")
Phys.Rev. D97 (2018) no.10, 106012

arXiv:1710.04669 [hep-th]

Benjamin Knorr (2017)

Infinite order quantum-gravitational correlations
Class.Quant.Grav. 35 (2018) no.11, 115005

arXiv:1710.07055 [hep-th]

Derives the flow equation, and fixed points, for the potential for the trace of the fluctuation and for a term linear in the square of the trace of the fluctuation, multiplied by an arbitrary function of the trace.

Astrid Eichhorn, Aaron Held and Christof Wetterich (2017)

Quantum gravity predictions for the fine-structure constant
Phys.Lett. B782 (2018) 198-201

arXiv:1711.02949 [hep-th]

Nicolai Christiansen, Kevin Falls, Jan Pawlowski and Manuel Reichert (2017)

Curvature dependence of quantum gravity
Phys.Rev. D97 (2018) no.4, 046007 

arXiv:1711.09259 [hep-th]

Using an approximate curved space definition for the momentum integrations on a sphere, the running of the two- and three-point function is calculated, and from that the running of a background f(R) action.

Astrid Eichhorn, Yuta Hamada, Johannes Lumma and Masatoshi Yamada (2017)

Quantum gravity fluctuations flatten the Planck-scale Higgs potential
Phys.Rev. D97 (2018) no.8, 086004

arXiv:1712.00319 [hep-th]

Sumarna Haroon, Mubasher Jamil,  Kai Lin, Petar Pavlovic, Marko Sossic and Anzhong Wang (2017)

The Effects of Running Gravitational Coupling On Rotating Black Holes
Eur.Phys.J. C78 (2018) 519

arXiv:1712.18762 [gr-qc]


Kevin Falls, Callum R. King, Daniel F. Litim Kostas Nikolakopoulos and Christoph Rahmede (2018)

Asymptotic safety of quantum gravity beyond Ricci scalars
Phys.Rev. D97 (2018) no.8, 086006 

arXiv:1801.00162 [hep-ph]

Tim R. Morris (2018)

Renormalization group properties in the conformal sector: towards perturbatively renormalizable quantum gravity
JHEP 1808 (2018) 024
arXiv:1802.04281 [hep-th]

Astrid Eichhorn, Aaron Held and Peter Vander Griend (2018)

Asymptotic safety in the dark
JHEP 1808 (2018) 147

arXiv:1802.08589 [hep-th]

Natalia Alkofer and Frank Saueressig (2018)

Asymptotically safe f(R)-gravity coupled to matter I: the polynomial case
Annals Phys. 396 (2018) 173-201

arXiv:1802.00498 [hep-th]

Alfio Bonanno, Alessia Platania and Frank Saueressig (2018)

Cosmological bounds on the field content of asymptotically safe gravity–matter models
Phys.Lett. B784 (2018) 229-236

arXiv:1803.02355 [gr-qc]

Astrid Eichhorn, Peter Labus, Jan Pawlowski and Manuel Reichert (2018)

Effective universality in quantum gravity
Phys.Rev. D94 (2016) no.2, 024007
arXiv:1804.00012 [hep-th]

Matthew P. Kellett, Tim R. Morris (2018)

Renormalization group properties of the conformal mode of a torus
Class.Quant.Grav. 35 (2018) no.17, 175002
arXiv:1803.00859 [hep-th]

Carlo Pagani and Martin Reuter (2018)

Finite Entanglement Entropy in Asymptotically Safe Quantum Gravity
JHEP 1807 (2018) 039
arXiv:1804.02162 [hep-th]

Benjamin Knorr and  Frank Saueressig (2018)

Towards reconstructing the quantum effective action of gravity
Phys.Rev.Lett. 121 (2018) no.16, 161304

arXiv:1804.03846 [hep-th]

Gustavo Pazzini De Brito, Nobuyoshi Ohta, Antonio Duarte Pereira and Anderson Tomasz (2018)

Asymptotic safety and field parametrization dependence in the f(R) truncation
Phys.Rev. D98 (2018) no.2, 026027 
arXiv:1805.09656 [hep-th]

Gabriele Gionti (2018)

Hamiltonian Analysis of Asymptotically Safe Gravity

arXiv:1805.10580 [astro-ph.CO]

Natalia Alkofer (2018)

Asymptotically safe f(R)-gravity coupled to matter II: global solutions
arXiv:1809.06162 [hep-th]

Simon Friederich

The asymptotic safety scenario for quantum gravity – An appraisal
Stud.Hist.Philos.Mod.Phys. 63 (2018) 65-73

K. Falls, D. Litim, K. Nikolakopulos and J. Schroeder (2018)

Aspects of asymptotic safety for quantum gravity

arXiv:1810.08550 [gr-qc]

Earlier results for the polynomial approximation of f(R) gravity are pushed to order 70.

Astrid Eichhorn, Stefan Lippoldt, Jan Pawlowski, Manuel Reichert and Marc Schiffer (2018)

How perturbative is quantum gravity?
Phys.Lett. B792 (2019) 310-314
arXiv:1810.02828 [hep-th]

Astrid Eichhorn (2018)

An asymptotically safe guide to quantum gravity and matter
Front.Astron.Space Sci. 5 (2019) 47
arXiv:1810.07615 [hep-th]

Jan.M. Pawlowski, Manuel Reichert, Christof Wetterich, Masatoshi Yamada (2018)

Higgs scalar potential in asymptotically safe quantum gravity
Phys.Rev. D99 (2019) no.8, 086010
arXiv:1811.11706 [hep-th]

Astrid Eichhorn, Marc Schiffer (2019)
d=4 as the critical dimensionality of asymptotically safe interactions
arXiv:1902.06479 [hep-th]

Gustavo P. De Brito, Yuta Hamada, Antonio D. Pereira, Masatoshi Yamada

On the impact of Majorana masses in gravity-matter systems
arXiv:1905.11114 [hep-th]

Christof Wetterich (2019)

Quantum scale symmetry
arXiv:1901.04741 [hep-th]

Christof Wetterich, Masatoshi Yamada (2019)

Variable Planck mass from gauge invariant flow equation
arXiv:1906.01721 [hep-th]

Carlo Pagani, Martin Reuter (2019)

Background Independent Quantum Field Theory and Gravitating Vacuum Fluctuations

Phys. Rev. D60, 084011

arXiv:1906.02507 [hep-th]

Benjamin Knorr, Chris Ripken and Frank Saueressig (2019)

Form factors in asymptotic safety: conceptual ideas and computational toolbox
Class.Quant.Grav. 36 (2019) no.23, 234001

arXiv:1907.02903 [hep-th]

Senarath de Alwis, Astrid Eichhorn, Aaron Held, Jan Pawlowski, Marc Schiffer and Fleur Versteegen (2019)

Asymptotic safety, string theory and the weak gravity conjecture
Phys.Lett. B798 (2019) 134991
arXiv:1907.07974 [hep-th]

Gustavo P. De Brito, Astrid Eichhorn, Antonio D. Pereira (2019)

A link that matters: towards phenomenological tests of unimodular asymptotic safety
JHEP 1909 (2019) 100
arXiv:1907.11173 [hep-th]

Astrid Eichhorn, Aaron Held, Christof Wetterich (2019)
Predictive power of grand unification from quantum gravity
arXiv:1909.17318 [hep-th]

John Donoghue (2019)

A critique of the asymptotic safety program

arXiv:1911.02967 [hep-th]

Applications of asymptotically safe gravity


Alfio Bonanno, Martin Reuter (1999)

Quantum gravity effects near the null black hole singularity.

Phys. Rev. D60, 084011



Alfio Bonanno, Martin Reuter (2000)

Renormalization group improved black hole spacetimes.

Phys. Rev. D 62, 043008.



This paper discusses the geometry of a black hole taking into account the RG flow of Newton's constant. In analogy to Uehling's treatment of the potential for a quantum electron, it is postulated that the main effect can be modelled by replacing G with G(k) where k=1/r.


Alfio Bonanno and Martin Reuter (2002)

Cosmology of the Planck era from a renormalization group for quantum gravity.

Phys. Rev. D 65, 043508.



The fixed point behaviour is applied to the early universe. The logic is similar to that of Bonanno and Reuter 2000, but here k is chosen to be 1/t, where t is the cosmic time.


Alfio Bonanno, Martin Reuter (2002)

Cosmology with selfadjusting vacuum energy density from a renormalization group fixed point.

Phys. Lett. B527, 9-17



Alfio Bonanno, Martin Reuter (2002)

Cosmological perturbations in renormalization group derived cosmologies.

Int. J. Mod. Phys. D13, 107-122 (2004)



Eloisa Bentivegna, Alfio Bonanno, Martin Reuter (2002)

Confronting the IR Fixed Point Cosmology with High Redshift Observations

JCAP 0401, 001 (2004)

arXiv: astro-ph/0303150


Martin Reuter and Holger Weyer (2004a)

Quantum gravity at astrophysical distances?

JCAP 0412, 001



It is shown that the real world may be modelled on a specific trajectory of the RG flow in the Einstein-Hilbert truncation. Point on the trajectory are associated to specific energy scales. The trajectories that resemble the real world automatically have a very small cosmological constant.


Martin Reuter, Holger Weyer (2004b)

Renormalization group improved gravitational actions: A Brans-Dicke approach.

Phys. Rev. D69, 104022



Martin Reuter and Holger Weyer (2004c)

Running Newton constant, improved gravitational actions, and galaxy rotation curves.

Phys.Rev.D70, 124028

arXiv: hep-th/0410117


Martin Reuter and Frank Saueressig (2005)

From big bang to asymptotic de Sitter: Complete cosmologies in a quantum gravity framework.

JCAP 09, 012.



A detailed analysis of cosmological models with varying Lambda and G. The energy momentum tensor of matter is required to be separately conserved. The cutoff identification is adjusted so that the modified Friedmann equations have a solution.


B.F.L. Ward (2006)

Planck Scale Remnants in Resummed Quantum Gravity

Acta Phys. Polon. B37, 1967-1974

arXiv: hep-ph/0605054


Hiroki Emoto (2005)

Asymptotic safety of quantum gravity and improved spacetime of black hole singularity by cutoff identification.



Hiroki Emoto (2006)

Quantum Gravity Through Non-Perturbative Renormalization Group and Improved Black Hole.



Alfio Bonanno, Martin Reuter (2006)

Spacetime structure of an evaporating black hole in quantum gravity.

Phys. Rev. D73, 083005

arXiv: hep-th/0602159


Martin Reuter and E. Tuiran (2006)

Quantum Gravity Effects in Rotating Black Holes

Proceedings of the 11th Marcel Grossmann Meeting (Berlin 2006)



Florian Girelli, Stefano Liberati, Roberto Percacci, Christoph Rahmede (2007)

Modified Dispersion Relations from the Renormalization Group of Gravity.

Class. Quant. Grav. 24, 3995-4008



A relation is suggested between the RG flow of gravitational couplings and the possibility of modified dispersion relations in quantum gravity.


Martin Reuter, Holger Weyer (2006)

On the Possibility of Quantum Gravity Effects at Astrophysical Scales.

Int. J. Mod. Phys. D15, 2011-2028



Alfio Bonanno, Martin Reuter (2007)

Entropy signature of the running cosmological constant.

JCAP 0708, 024

arXiv:0706.0174 [hep-th]


Contrary to earlier applications of the RG in a cosmological context, here one does not require separately the conservation of the energy momentum tensor. Thus there can bean effective flow of energy between the varying couplings (Lambda and G) and matter. It is shown that the decaying cosmological constant can generate the right amount of entropy that is observed in the universe. The cutoff identification is k=Hubble parameter.


JoAnne Hewett, Thomas Rizzo (2007)

Collider Signals of Gravitational Fixed Points.

JHEP 0712, 009

arXiv:0707.3182 [hep-ph]


The scale dependence of Newton's constant in asymptotically safe gravity is parametrized by a form factor. Consequences are worked out for several processes that may occur at colliders, either with large extra dimensions or warped extra dimensions.


Daniel F. Litim and Tilman Plehn (2008)

Signatures of gravitational fixed points at the LHC.

Phys. Rev. Lett. 100, 131301

arXiv:0707.3983 [hep-ph]


Takes into account the asymptotically safe behaviour of Newton’s constant in graviton-mediated Drell-Yan processes.


Daniel F. Litim and Tilman Plehn (2007)

Virtual gravitons at the LHC.

arXiv:0710.3096 [hep-ph]


In the proceedings of 15th International Conference on Supersymmetry and the Unification of Fundamental Interactions (SUSY07), Karlsruhe, Germany, 26 Jul - 1 Aug 2007.


Ben Koch (2007)

Black Hole Resonances or no Black Holes due to Large Extra Dimensions with Gravitational Fixed Point?

Phys. Lett. B663, 334-337 (2008)

arXiv:0707.4644 [hep-ph]


Calculates the effect of the running G near a FP on the black hole production cross section in models with large extra dimensions.


B.F.L. Ward (2008)

Planck Scale Cosmology in Resummed Quantum Gravity.,

Mod. Phys. Lett. A23, 3299-3305

arXiv:808.3124 [gr-qc]


Alfio Bonanno, Martin Reuter (2008)

Primordial Entropy Production and Lambda-driven Inflation from Quantum Einstein Gravity.

J. Phys. Conf. Ser.140, 012008

arXiv:0803.2546 [hep-th]


B.F.L. Ward (2009)

Planck Scale Cosmology and Resummed Quantum Gravity.,

in the proceedings of DPF-2009, Detroit, MI, July 2009, eConf C090726; 3



Steven Weinberg (2009)
Asymptotically safe inflation

Phys. Rev. D81 083535 (2010)

arXiv:0911.3165 [hep-th]


The conditions for a long almost de Sitter phase are discussed in the context of a general gravitational action near a fixed point.


Mikhail Shaposhnikov and Christof Wetterich (2009)

Asymptotic safety of gravity and the Higgs boson mass

Phys. Lett. B683 196-200 (2010)

arXiv:0912.0208 [hep-th]


It is shown that with certain assumptions it is possible to derive predictions for the Higgs mass from the hypothesis of asymptotic safety of gravity plus the standard model.

Martin Reuter and E. Tuiran (2009)

Quantum Gravity Effects in the Kerr spacetime
Phys. Rev. D83, 044041 (2011)


This paper considers the properties of "RG improved" Kerr spacetimes.

Kevin Falls, Daniel F. Litim and Aarti Raghuraman (2010)

Black holes and asymptotically safe gravity
Int. J. Mod. Phys. A27 1250019 (2012)

arXiv:1002.0260 [hep-ph]


Discuss the effect of asymptotic safety on black holes in various dimensions. Calculate the production cross section for black holes at colliders.


Sayandeb Basu and David Mattingly (2010)

Asymptotic Safety, Asymptotic Darkness, and the hoop conjecture in the extreme UV.
Phys. Rev. D82, 124017 (2010)

arXiv:1006.0718 [hep-th]


Modify the proof of the hoop conjecture taking into account the fixed point behaviour of Newton’s constant,

and find that if G<2  black holes not to form.


Yi-Fu Cai and Damien Easson (2010)

Black holes in an asymptotically safe gravity theory with higher derivatives.
JCAP 1009, 002 (2010)

arXiv:1007.1317 [hep-th]


These authors discuss the spherically symmetric black hole solutions in a truncation containing also four-derivative terms. The identification of the cutoff is different from the preceding paper.


Alfio Bonanno, Adriano Contillo and Roberto Percacci (2010)

Inflationary solutions  in asymptotically safe f(R) gravity
Class. and Quantum Grav. 28, 145026 (2011)

arXiv:1006.0192 [gr-qc]


This paper discusses the existence of inflationary (exponential or power law) cosmological solutions in a class of renormalization group improved polynomial f(R) theonly with matter. The nonconservation of the energy momentum tensor is also discussed.


B.F.L. Ward (2010a)

An estimate of \Lambda in Resummed Quantum Gravity in the context of asymptotic safety

arXiv:1008.1046 [gr-qc]


Roberto Casadio, Stephen Hsu and Behrouz Mirza (2010)

Asymptotic safety, singularities and gravitational collapse
Phys. Lett. B695, 317-319 (2011)

arXiv:1008.2768 [gr-qc]

These authors analyse the issue of the formation of a singularity in the collapse of a thin shell, taking into account the running of Newton's constant. The cutoff is related to the matter density. Conditions for the avoidance of a singularity are discussed.

Xavier Calmet, Sabine Hossenfelder and Roberto Percacci (2010)

Deformed special relativity and asymptotically safe gravity
Phys. Rev. D82, 124024

arXiv:1008.3345 [gr-qc]


The possibility of a deformation of the action of the Lorentz group is analyzed, taking into account renromalization group running of Newton's constant. It is suggested that asymptotic safety could lead to a kind of deformation, but only in the case of virtual particles.

S.H. Henry Tye and Jiajun Xu (2010)

Comments on asymptotically safe inflation
Phys. Rev. D82, 127302 (2010)

arXiv:1008.4787 [hep-th]

These authors repeat the analysis of Weinberg 2009. They point out that inflation occurs sufficiently below the Planck scale that the couplings are not at their fixed point values. They confirm the necessity of fine tuning.

B.F.L. Ward (2010b)

Planck scale cosmology and asymptotic safety in Resummed Quantum Gravity
PoS ICHEP 2010:477 (2010)

arXiv:1012.2680 [gr-qc]

Eric Gerwick, Daniel F. Litim and Tilman Plehn (2011)

Asymptotic safety and Kaluza-Klein gravitons at the LHC.
Phys. Rev. D83 084048 (2011)

arXiv:1101.5548 [hep-ph]

This paper explores in detail the theory and phenomenology of Drell-Yan processes in the large extra dimensions scenario. It extends previous work by Hewett and Rizzo and Litim and Plehn.

Mark Hindmarsh, Daniel Litim and Christoph Rahmede (2011)

Asymptotically safe cosmology
JCAP 1107, 019 (2011)

arXiv:1101.5401 [gr-qc]


In this paper the cutoff is allowed to depend on time and the energy momentum tensor is assumed to be conserved. This put constraints on the form of the cutoff. The field equations and the RG equations are written as a coupled autonomous system. Various classes of solutions of these equations are discussed.

Changrim Ahn, Chanju Kim and Eric V. Linder (2011)

From asymptotic safety to dark energy
Phys. Lett. B704 10-14 (2011)

arXiv:1106.1435 [astro-ph.CO]

Rong-Jia Yang (2011)

Asymptotically safe phantom cosmology

arXiv:1108.0227 [gr-qc]

Yi-Fu Cai and Damien Easson (2011)

Asymptotically safe gravity as a scalar-tensor theory and its cosmological implications
Phys. Rev. D84, 103502 (2011)

arXiv:1107.5815 [hep-th]

Adriano Contillo, Mark Hindmarsh and Christoph Rahmede (2011)

Renormalization group improvement of scalar field inflation
Phys. Rev. D85, 043501 (2012)

arXiv:1108.0422 [gr-qc]


Sungwook E. Hong, Young Jae Lee, Heeseung Zoe (2011)

The Possibility of Inflation in Asymptotically Safe Gravity

arXiv:1108.5886 [gr-qc]

Alfio Bonanno (2012)

An effective action for asymptotically safe gravity
Phys.Rev. D85 (2012) 081503

arXiv:1203.1962 [hep-th]


It is argued that the so called "RG improvement" i.e. the replacement of the cutoff scale k by a physical parameter of the problem, should be performed in the action, rather than the equations of motion. This is in line with examples from QCD. It is assumed that the cutoff is proportional to the square root of R. When substituted in the Einstein-Hilbert action this leads to a kind of f(R) theory. This is analyzed in the vicinity of the fixed point, the flow can be solved by linearization and consists of spiralling trajectories. The effective theory contains a term of the form cos log R. It is shown that there exist infinitely many de Sitter solutions, some being stable and others unstable. In particular there are unstable solutions with sufficient e-foldings to produce inflation.

Mark Hindmarsh and Ippocrates Saltas (2012)

f(R) gravity from the renormalisation group
Phys.Rev. D86 (2012) 064029

arXiv:1203.3857 [gr-qc]


As in the preceding paper, the cutoff is identified with the square root of R in the action, up to a factor r. The resulting theory is then analyzed by going to the Einstein frame. As in the preceding paper, infinitely many de Sitter solutions are found. In the Lambda-G plane, the evolution of the universe would correspond to the piece of RG trajectory that starts from an "outer" de Sitter solution in the UV (i.e. in the past, producing inflation), passes near the Gaussian fixed point and then approaches another de Sitter point (accelerated expansion). Viability of the picture in the classical regime requires r near one, but this would lead to excessive primordial fluctuations. Viability of the inflationary phase requires a large r. It is suggested that this discrepancy may be solved in the presence of additional degrees of freedom.

Babette Dobrich and Astrid Eichhorn (2012)

Can we see quantum gravity? Photons in the asymptotic-safety scenario.
JHEP 206, 156 (2012)

arXiv:1203.6366 [hep-th]


Photon-photon scattering is proposed as a possible experimental signature of quantum gravitational effects in higher dimensional scenarios.

Fedor Bezrukov, Mikhail. Yu. Kalmykov, Bernd A. Diehl and Mikhail Shaposhnikov (2012)

Higgs boson mass and new physics
JHEP 1210 (2012) 140

arXiv:1205.2893 [hep-th]


This paper elaborates the prediction of a Higgs boson near the lower mass bound, originally presented in Shaposhnikov and Wetterich (2009). Three loop beta functions are used for the low energy domain. Asymptotic safety arguments are used to predict the Higgs mass to be 129 +/- 6 GeV. It is argued that the discovery of a Higgs with this mass would point towards the absence of intermediate scales between the Fermi and the Planck scale, and may actually point towards a connection between the two.

Christopher Estrada and Matilde Marcolli (2012)

Asymptotic safety, hypergeometric functions and the Higgs mass in spectral action models
Int.J.Geom.Meth.Mod.Phys. 10 (2013) 1350036

arXiv:1208.5023 [hep-th]

Calculation of the running of the Higgs self-coupling taking into account gravitational corrections in a noncommutative model.

Anja Marunovic and Tomislav Prokopec (2012)

On antiscreening in perturbative quantum gravity and resolving the Newtonian singularity

arXiv:1209.4779 [hep-th]


Chao Fang and Quin-Guo Huang (2012)

The trouble with asymptotically safe inflation.

arXiv:1210.7596 [hep-th]

Kevin Falls and Daniel F. Litim (2012)

Black hole thermodynamics under the microscope
Phys.Rev. D89 (2014) 084002

arXiv:1212.1821 [hep-ph]

Yi-Fu Cai, Yo-Chao Chang, Pisin Chen, Damien Easson and Taotao Qiu (2013)

Planck constraints on Higgs modulated reheating of renormalization group improved inflation
Phys.Rev. D88 (2013) 083508

arXiv:1304.6938 [hep-th]

T. Henz, J. Pawlowski, A. Rodigast and C. Wetterich (2013)

Dilaton quantum gravity

arXiv:1304.7743 [hep-th]

Edmund Copeland, Christoph Rahmede and Ippocratis Saltas (2013)

Asymptotically safe Starobinski inflation

arXiv:1311.0881 [gr-qc]


This paper deals with effective actions of the form R+R^2. The beta functions are shown to have a nontrivial fixed point where the R^2 term is asymptotically free (as in one-loop calculations). It is shown that there are RG trajectories that describe well Starobinski inflation. In particular the value of the R^2 coupling at the Planck scale is determined from CMB data. It is shown to be of order 10^(-9).

Benjamin Koch, and Frank Saueressig (2013)

Structural aspects of asymptotically safe black holes.
Class. and Quantum Grav. 31 (2013) 015006

arXiv:1306.1546 [hep-th]


This paper deals with the "RG improvement" of the Schwarzschild-de Sitter solution.

The results differ significantly from the RG improvement of the ordinary Schwarzschild solutions,

because here the cosmological constant enters in a nontrivial way. The cutoff is identified with
a (multiple of) radial distance from the origin and the resulting spacetime-dependent couplings
are used in the solution. At the nontrivial fixed point, the improved solution has exactly the
same form as the classical one, but the role of the cosmological and Newton couplings are
reversed. As a consequence, the singularity in the origin is not removed.

The thermodynamics of these black holes is studied. The entropy is shown to correspond to
the effective average action evaluated at a self-consistent solution. This suggests that the
microscopic origin of the black hole entropy is in the fluctuations of the geometry.

Benjamin Koch, Carlos Contreras, Paola Rioseco and Frank Saueressig (2013)

Black holes and running couplings: a comparison of two complementary approaches
Springer Proc.Phys. 170 (2016) 263-269

arXiv:1311.1121 [hep-th]

Proceedings of the Karl Schwarzschild meeting, Frankfurt am Main, July 22-26, 2013.

C. Wetterich (2014)

Inflation, quintessence and the origin of mass
Nucl.Phys. B897 (2015) 111-178

arXiv:1408.0156 [hep-th]

Benjamin Koch, Paola Rioseco (2014)

Scale Setting for Self-consistent Backgrounds
Phys.Rev. D91 (2015) no.2, 025009

arXiv:1409.4443 [hep-th]

Benjamin Koch, Paola Rioseco (2015)

Black Hole Solutions for Scale Dependent Couplings: The de Sitter and the Reissner-Nordström Case
Class.Quant.Grav. 33 (2016) 035002 

arXiv:1501.00904 [hep-th]

Georgios Kofinas, Vasilios Zarikas (2015)

Avoidance of singularities in asymptotically safe Quantum Einstein Gravity
JCAP 1510 (2015) no.10, 069

arXiv:1506.02965 [hep-th]

Zhong-Zhi Xianyu and Hong-Jian He (2014)

Asymptotically safe Higgs inflation

arXiv:1407.6993 [hep-ph.CO]

Alfio Bonanno and Alessia Platania (2015)

Asymptotically safe inflation from quadratic gravity
Phys.Lett. B750 (2015) 638-642

arXiv:1507.03375 [gr-qc]

Georgios Kofinas, Vasilios Zarikas (2015)

Asymptotically Safe gravity and non-singular inflationary Big Bang with vacuum birth
Phys.Rev. D94 (2016) no.10, 103514

arXiv:1605.02241 [hep-th]

Carlos Contreras, Benjamin Koch, Paola Rioseco (2016)

Setting the Renormalization Scale in QFT
J.Phys.Conf.Ser. 720 (2016) no.1, 012020

K. Falls, D. Litim, K. Nikolakopulos and C. Rahmede (2016)

On de Sitter solutions in asymptotically safe f(R) theories
Class.Quant.Grav. 35 (2018) no.13, 135006

arXiv:1607.04962 [hep-th]

A detailed discussion of the existence of De Sitter solution in the f(R) approximation, using high order polynomial expansion and various resummation methods. Contrary to Bonanno, Contillo and Percacci (2010), a De Sitter solution is not found.

Alfio Bonanno, Benjamin Koch and Alessia Platania (2016)

Cosmic Censorship in Quantum Einstein Gravity
Class.Quant.Grav. 34 (2017) no.9, 095012

arXiv:1610.05299 [gr-qc]

Christof Wetterich and Masatoshi Yamada (2016)

Gauge hierarchy problem in asymptotically safe gravity - the resurgence mechanism
Phys.Lett. B770 (2017) 268-271

arXiv:1612.03069 [hep-th]

Alfio Bonanno and Frank Saueressig (2017)

Asymptotically safe cosmology - a status report
Comptes Rendus Physique 18 254-264

arXiv:1702.04137 [hep-th]

Alfio Bonanno, Benjamin Koch and Alessia Platania (2017)

Asymptotically Safe gravitational collapse: Kuroda-Papapetrou RG-improved model
PoS CORFU2016 (2017) 058

R. Moti, A. Shojai (2017)

On the effect of renormalization group improvement on the cosmological power spectrum
Eur.Phys.J. C78 (2018) no.1, 32

arXiv:1703.02733 [gr-qc]

Ramon Torres (2017)

Nonsingular black holes, the cosmological constant, and asymptotic safety
Phys.Rev. D95 (2017) no.12, 124004

arXiv:1703.09997 [hep-th]

It is shown that the usual procedure of identifying the cutoff with the inverse distance from the center of a spherically symmetric solution, and then "improving" the black hole solution by replacing G by the running G, leads to regular solutions in the case of unimodular gravity. The residual singularities that appeared in earlier works was due to the behavior of the cosmological term.

Georgios Kofinas, Vasilios Zarikas (2017)

A solution of the dark energy and its coincidence problem based on local antigravity sources without fine-tuning or new scales
Phys. Rev. D 97, 123542 (2018)

arXiv:1706.08779 [hep-th]

Alfio Bonanno, Gabriele Gionti and Alessia Platania (2017)

Bouncing and emergent cosmologies from ADM RG flows

arXiv:1710.06317 [hep-th]

Astrid Eichhorn, Aaron Held (2018)

Mass difference for charged quarks from quantum gravity
Phys.Rev.Lett. 121 (2018) no.15, 151302

arXiv:1803.04027 [hep-th]

Astrid Eichhorn, Aaron Held and Christof Wetterich (2017)

Quantum-gravity predictions for the fine-structure constant
Phys.Lett. B782 (2018) 198-201

arXiv:1711.02949 [hep-th]

Abishek Majhi (2018)

Singularity from star collapse, torsion and asymptotic safety of gravity

arXiv:1804.00960 [gr-qc]

Yuexin Zhang, Menglei Zhou and Cosimo Bambi (2018)

Iron line spectroscopy of black holes in asymptotically safe gravity
Eur.Phys.J. C78 (2018) no.5, 376

arXiv:1804.07955 [gr-qc]

Lei-Hua Liu, Tomislav Prokopec and Alexei Starobinsky (2018)

Inflation in an effective gravitational model & asymptotic safety
Phys.Rev. D98 (2018) no.4, 043505 

arXiv:1806.05407 [gr-qc]

Giulia Gubitosi, Robin Ooijer, Chris Ripken, and Frank Saueressig (2018)

Consistent early and late time cosmology from the RG flow of gravity

arXiv:1806.10147 [hep-th]

Fotios K. Anagnostopoulos, Spyros Basilakos, Georgios Kofinas, Vasilios Zarikas (2018)

Constraining the Asymptotically Safe Cosmology: cosmic acceleration without dark energy

arXiv:1806.10580 [astro-ph.CO]

Giulia Gubitosi, Robin Oojer, Chris Ripken and Frank Saueressig (2018)

Consistent early and late time cosmology from the RG flow of gravity
JCAP 1812 (2018) no.12, 004

arXiv:1806.10147 [hep-th]

Jan Kwapisz and Frederic Grabowski (2018)

Asymptotic safety, cosmology and Conformal Standard Model

Proceedings of the 15th Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Astrophysics, and Relativistic Field Theories (MG15)

Jan M. Pawlowski, Dennis Stock (2018)

Quantum-improved Schwarzschild-(A)dS and Kerr-(A)dS spacetimes
Phys.Rev. D98 (2018) no.10, 106008

arXiv:1807.10512 [gr-qc]

Vasilios Zarikas and Georgios Kofinas (2018)

Singularities and Phenomenological aspects of Asymptotic Safe Gravity
J.Phys.Conf.Ser. 1051 (2018) no.1, 012028

C17-17-03.17 Proceedings

Ademola Adeifoba, Astrid Eichhorn and Alessia Platania (2018)

Towards conditions for black-hole singularity-resolution in asymptotically safe quantum gravity 

arXiv:1808.03472 [gr-qc]

Frederic Grabowski, Jan H. Kwapisz and Krysztof Meissner (2018)

Asymptotic safety and conformal standard model

arXiv:1810.08461 [hep-ph]

Astrid Eichhorn, Stefan Lippoldt, Marc Schiffer (2018)

Zooming in on fermions and quantum gravity

arXiv:1812.08782 [gr-qc]

Frank Saueressig, Giulia Gubitosi, Chris Ripken (2019)

Scales and hierachies in asymptotically safe quantum gravity: a review

arXiv:1901.01731 [hep-th]

Astrid Eichhorn, Marc Schiffer (2019)

d=4 as the critical dimensionality of asymptotically safe interactions

arXiv:1902.06479 [gr-qc]

Lando Bosma, Benjamin Knorr and Frank Saueressig (2019)
Resolving Spacetime Singularities within Quantum Gravity

arXiv:1904.04845 [hep-th]

Aaron Held, Roman Gold, Astrid Eichhorn (2019)

Asymptotic safety casts its shadow

arXiv:1904.07133 [gr-qc]

Alessia Platania (2019)

The inflationary mechanism in Asymptotically Safe Gravity

arXiv:1908.03897 [gr-qc]

Other nonperturbatively renormalizable theories and applications

Giorgio Parisi (1975)

The Theory of Nonrenormalizable Interactions. 1. The Large N Expansion

Nucl. Phys. B100 368

K. Gawedzki, A. Kupiainen (1985c)

Rigorous Renormalization Group - Asymptotic Freedom And Nongaussian Fixed Points.

In *Boulder 1983, Proceedings, Mathematical Physics Vii*, 455-464.

K. Gawedzki, A. Kupiainen (1985b)

Renormalization Of A Nonrenormalizable Quantum Field Theory.

Nucl.Phys.B262 33

K. Gawedzki, A. Kupiainen (1985a)

Renormalizing The Nonrenormalizable.

Phys. Rev. Lett. 55  363-365

In these papers the Gross-Neveu model in two dimensions, with p-2+ε propagator is shown to be renormalizable at a nonperturbative fixed point.

C. de Calan, P.A. Faria da Veiga, J. Magnen, R. Seneor (1991)

Constructing the three-dimensional Gross-Neveu model with a large number of flavor components.

Phys. Rev. Lett. 66 3233-3236

An example of a perturbatively nonrenormalizable theory that is nonperturbatively renormalizable, asymptotically safe at a nongaussian UV fixed point.

D.I. Kazakov (2003).

Ultraviolet fixed points in gauge and SUSY field theories in extra dimensions.

JHEP 03, 020.


Holger Gies (2003)

Renormalizability of gauge theories in extra dimensions.

Phys. Rev. D68, 085015


These two papers point out that gauge theories in more that four dimensions could have nontrivial fixed points.

Alessandro Codello and Roberto Percacci (2008)

Fixed Points of Nonlinear Sigma Models in d>2.

Phys. Lett. B672, 280-283 (2009)

arXiv:0810.0715 [hep-th]

It is shown that in the simplest truncation containing only the term with two derivatives, the ERGE gives a Ricci-type flow for the internal metric of the nonlinear sigma model, in any dimension >2 (it is not a Ricci flow proper because of the appearance of the independent variable in the r.h.s. due to dimensional reasons; proper Ricci flow is obtained only in 2 dimensions). In the O(N) model there seems to be a fixed point of the type needed for asymptotic safety.

Holger Gies, Michael M. Scherer (2009a)

Asymptotic safety of simple Yukawa systems.

Eur. Phys. J. C66, 387-402 (2010)

arXiv:0901.2459 [hep-th]

This paper finds a fixed point in a Yukawa theory with a single scalar, for small noninteger number of fermions. Since the fixed point arises from a balance between fermion and boson contributions, this implies that more realistic models with more bosonic degrees of freedom are also likely to have such a fixed point. Implications for the triviality and hierarchy problem are pointed out.

Holger Gies, Stefan Rechenberger and Michael M. Scherer (2009b)

Towards an Asymptotic-Safety Scenario for Chiral Yukawa Systems.
Eur. Phys. J. C66, 403-418 (2010)

arXiv:0907.0327 [hep-th]

The results of the previous paper are extended to the case when there is one right handed fermion and N left handed fermions. Various fixed points are found and their properties discussed.

Michael M. Scherer , Holger Gies and Stefan Rechenberger (2009c)

An asymptotic-safety mechanism for chiral Yukawa systems.
Acta Phys. Polon.  supp. , 541 (2009)

arXiv:0910.0395 [hep-th]

Talk presented at the Cracow School of Theoretical Physics, XLIX Course, Zakopane, Poland, May 31 - June 10, 2009.

A discussion of the Gross-Neveu model using modern functional RG methods.

Roberto Percacci and Omar Zanusso (2009)

One loop beta functions and fixed points in Higher Derivative Sigma Models

Phys. Rev. D81 065012 (2010)

arXiv:0910.0851 [hep-th]

Extends the results of Codello and Percacci (2008) to higher derivative terms.
The calculation is done in full detail for the O(N) models and for chiral models. Fixed points are found in some cases and not in others.

Holger Gies and Lukas Janssen (2010)

UV fixed point structure of the three dimensional Thirring model
Phys. Rev. D82
, 085018, 2010

arXiv:1006.3747 [hep-th]

This paper contains an analysis of the flow of three-dimensional four-fermion couplings in a theory with N flavors. From the assumed symmetries, and up to Fierz rearrangements, two couplings are studied: one is the vector coupling as in the Thirring model, the other a scalar coupling. Four fixed points are found. In the large N limit one of these purely of Thirring type, in accordance with previous large N studies. For small N this fixed point comes close to being of Nambu-Jona-Lasinio type. The question whether there exists a critical value of N (above which no breaking of the "chiral" symmetry is possible) is hard to address reliably in this formalism.

Jens Braun, Holger Gies and Daniel D. Scherer (2010)

Asymptotic safety: a simple example.
Phys. Rev. D83, 085012 (2011)

arXiv:1011.1456 [hep-th]

Here a similar analysis is performed for the Gross-Neveu model, where the four-fermion interaction contains two scalar bilinears.

Holger Gies and Lukas Janssen (2012)

Critical behavior of (2+1)-dimensional Thirring model
Phys. Rev. D86
, 105007, 2012

arXiv:1208.3327 [hep-th]

This paper continues the analysis of Gies and Janssen (2010) but this time using partial bosonization (i.e. bosonic condensates are introduced as independent fields). It is found that reliable results require dynamical bosonization, i.e. the four-fermion couplings that are regenerated by quantum fluctuations in the bosonized system have to be eliminated at each RG step by a Hubbard-Stratonovich transformation. With this technique the UV behavior of the purely fermionic system can be reproduced and the critical number of flavors is determined.

Marco Fabbrichesi, Roberto Percacci, Alberto Tonero and Omar Zanusso (2010)

Asymptotic safety and the SU(N) gauged nonlinear sigma model
Phys. Rev. D83,  025016 (2011)

arXiv:1010.0912 [hep-ph]

The beta functions of the left-gauged chiral model are computed in a truncated RG keeping the leading terms in the derivative expansion. The gauge coupling is asymptotically free and the sigma model coupling has a nontrivial fixed point in the same position as in the ungauged case.

Xavier Calmet (2010a)
An alternative view on the electroweak interactions

arXiv:1008.3780 [hep-ph]

Xavier Calmet (2010b)
Asymptotically safe weak interactions

arXiv:1008.3780 [hep-ph]

Marco Fabbrichesi, Roberto Percacci, Alberto Tonero and Luca Vecchi (2011)

The electroweak S and T parameters from a fixed point condition
Phys. Rev. Lett. 107 021803 (2011)

arXiv:1102.2113 [hep-ph]

It is shown first that if one considers the SU(2)-valued sigma model with SU(2)xU(1)-invariant metric, which is characterized by an overall scale and a squashing parameter, there are two fixed points: one with the usual bi-invariant metric and one with a specific squashing. In the standard model the squashing is related to the T-parameter. This result is extended to the SU(2)xU(1) gauged case, taking into account a further operator that corresponds to the S parameter. The renormalizable trajectories corresponding to the two fixed points are studied and it is found that there are trajectories that are compatible with electroweak precision data.

Federica Bazzocchi, Marco Fabbrichesi, Roberto Percacci, Alberto Tonero and Luca Vecchi (2011)

Fermions and Goldstone bosons in an asymptotically safe model

arXiv:1105.1968 [hep-ph]

It is shown first that realistic fermion content would destroy the fixed point that is present in the bosonic SU(2)xU(1) theory. The fixed point can be recovered by postulating the existence of four fermion interactions. Assuming that these interactions are SU(2)xSU(2) invariant, one has four independent structures, modulo Fierz transformations, and 16 fixed points.

Daniel Litim, Roberto Percacci and Leslaw Rachwal (2011)

Scale-dependent Planck mass and Higgs VEV from holography and functional renormalization

arXiv:1109.3062 [hep-th]

The system being studied here is the nonlinear sigma model coupled to gravity. It is shown that there is a nontrivial fixed point in the simplest truncation, involving only two-derivative terms both for gravity and for the scalars. The results of the functional RG are surprisingly similar to those of a "holographic" RG based on five-dimensional AdS space, possibly containing source brane a la Randall-Sundrum.

Raphael Flore, Andreas Wipf and Omar Zanusso (2012)

Functional renormalization group of the non-linear sigma model and the O(N) universality class

arXiv:1207.4499 [hep-th]

The nonlinear sigma model is studied in three dimensions keeping terms up to four derivatives. A fixed point is found in the presence of one of the four-derivative terms, but not of the other. Results for the O(N) phase diagram are compared with the existing literature.

Holger Gies, Stefan Rechenberger, Michael Scherer and Luca Zambelli (2011)

An asymptotic safety scenario for gauged chiral Higgs-Yukawa models.

Eur.Phys.J. C73 (2013) 2652

arXiv:1306.6508 [hep-th]

B. Wellegehausen, D. Koerner, A. Wipf (2014)

Asymptotic safety on the lattice: the O(N) sigma model

arXiv:1402.1851 [hep-lat]

D. Koerner,  B. Wellegehausen, Andreas Wipf (2014)

MCRG flow for nonlinear sigma model
PoS LATTICE2013 (2013) 052

Results from MonteCarlo simulations supporting the existence of a nontrivial fixed point in the nonlinear sigma model in three dimensions.

Daniel Litim and Francesco Sannino (2014)

Asymptotic safety guaranteed.
JHEP 1412 (2014) 178

arXiv:1406.2337 [hep-th]

Models of scalars, fermions and gauge fields in the Veneziano limit admit a nontrivial fixed point that can be studied in perturbation theory.

Francesco Sannino and Ian M. Shoemaker (2014)

Asymptotically safe dark matter
Phys.Rev. D92 (2015) no.4, 043518

arXiv:1412.8034 [hep-th]

J. Kovacs, S. Nagy, and K. Sailer (2014)

Asymptotic safety in the sine-Gordon model

arXiv:1408.2680 [hep-th]

Daniel Litim and Francesco Sannino (2015)

Vacuum stability of asymptotically safe gauge-Yukawa theories
JHEP 1601 (2016) 081

arXiv:1501.03061 [hep-th]

Holger Gies and Luca Zambelli (2015)

Asymptotically free scaling solutions in non-abelian Higgs models.

arXiv:1502.05907 [hep-th]

Niklas Gronlund Nielsen, Francesco Sannino and Ole Svendsen (2015)

Inflation from asymptotically safe theories
Phys.Rev. D91 (2015) 103521

arXiv:1503.00702 [hep-th]

Zhi-Wei Wang, Frederick S. Sage, T.G. Steele, R.B. Mann (2015)

Asymptotic Safety in the Conformal Hidden Sector?
J.Phys. G45 (2018) no.9, 095002 

arXiv:1511.02531 [hep-ph]

Andrew Bond and Daniel Litim (2016)

Theorems for asymptotic safety of gauge theories
Eur.Phys.J. C77 (2017) no.6, 429

arXiv:1608.00519 [hep-th]

Dirk H. Rischke and Francesco Sannino (2015)
Thermodynamics of asymptotically safe theories
Phys.Rev. D92 (2015) no.6, 065014
arXiv:1505.07828 [hep-th]

Borut Bajc and Francesco Sannino (2016)

Asymptotically safe Grand Unification

arXiv:1610.09681 [hep-th]

Giulio Maria Pelaggi, Francesco Sannino,Alessandro Strumia, Elena Vigiani (2017)

Naturalness of Asymptotically safe Higgs

arXiv:1701.01453 [hep-th]

Andrew Bond, Gudrun Hiller, Kamila Kowalska and Daniel Litim (2017)

Directions for model building from asymptotic safety
JHEP 1708 (2017) 004

arXiv:1702.01727 [hep-ph]

Steven Abel and Francesco Sannino (2017)

Radiative symmetry breaking from interacting UV fixed points

arXiv:1704.00700 [hep-th]

Giulio Maria Pelaggi, Alexis D. Plascencia, Alberto Salvio, Francesco Sannino, Yuri Smirnov, Alessandro Strumia (2018)

Asymptotically Safe Standard Model Extensions?
Phys.Rev. D97 (2018) no.9, 095013

arXiv:1708.00437 [hep-th]

R.B. Mann, J.R. Meffe, F. Sannino, T.G. Steele, Z.W. Wang and C. Zhang (2017)

Asymptotically safe Standard Model via vector-like fermions

arXiv:1707.02942 [hep-th]

Andrew Bond and Daniel Litim (2017)

More asymptotic safety guaranteed
Phys.Rev. D97 (2018) no.8, 085008

arXiv:1707.04217 [hep-th]

Andrew Bond and Daniel Litim (2017)

Asymptotic safety guaranteed in supersymmetry
Phys.Rev.Lett. 119 (2017) no.21, 211601

arXiv:1709.06953 [hep-th]

Daniele Barducci, Marco Fabbrichesi, Carlos Nieto, Roberto Percacci and Vedran Skrinjar (2018)

In search of a UV completion of the Standard Model - 378.000 models that don't work

arXiv:1107.05584 [hep-ph]

It is shown that a large number of extensions of the standard model by the addition of vector-like fermions, have non-trivial fixed points that either are not under perturbative control, or else exhibit the U(1) triviality problem.

Andrew Bond, Daniel Litim, Gustavo Medina Vazquez and Tom Steudtner (2017)

UV conformal window for asymptotic safety

Phys.Rev. D97 (2018) no.3, 036019

arXiv:1710.07615 [hep-th]

Daniel Litim and Matthew J. Trott (2018)

Asymptotic safety of scalar field theories

arXiv:1810.01678 [hep-th]

Andrew Bond and Daniel Litim (2018)

Price of asymptotic safety

arXiv:1801.08527 [hep-th]

Gudrun Hiller, Clara Hormigos-Feliu, Daniel F. Litim, Tom Steudtner  (2019)

Asymptotically safe extensions of the Standard Model with flavour phenomenology

arXiv:1905.11020 [hep-th]

Borut Bajc, Adrian Lugo and Francesco Sannino (2019)

Safe hologram

arXiv:1910.07354 [hep-th]

Andrew Bond, Daniel F. Litim, Tom Steudtner  (2019)

symptotic safety with Majorana fermions and new large N equivalences

arXiv:1911.11168 [hep-th]

  Classic papers on quantum gravity

Gerard 't Hooft, Martinus J.G. Veltman (1974)

One loop divergencies in the theory of gravitation.

Annales Poincare Phys.Theor.A20, 69-94

It is proven here that pure gravity is one-loop renormalizable but gravity coupled to a scalar field is not renormalizable at one loop.


S. Deser, and P. van Nieuwenhuizen, (1974a)

Nonrenormalizability of the Quantized Einstein-Maxwell System

Phys. Rev. Lett.32 245-247


S. Deser, and P. van Nieuwenhuizen, (1974b)

Nonrenormalizability of quantized fermion-gravitation interactions

Lett. Nuovo Cim. 11, 218-220


S. Deser, H.S. Tsao and P. van Nieuwenhuizen (1974a)

Nonrenormalizability of Einstein Yang-Mills Interactions at the One Loop Level

Phys. Lett. 50B, 491


S. Deser, and P. van Nieuwenhuizen (1974c)

One Loop Divergences of Quantized Einstein-Maxwell Fields
Phys. Rev. D10, 401


S. Deser, and P. van Nieuwenhuizen, (1974d)

Nonrenormalizability of the Quantized Dirac-Einstein System

Phys. Rev. D10, 411


S. Deser, H.S. Tsao and P. van Nieuwenhuizen (1974b)

One Loop Divergences of the Einstein Yang-Mills System

Phys. Rev. D10, 3337

These papers extend the result of ‘t Hooft and Veltman to the cases when matter consists of (abelian or nonabelian) gauge fields, or fermions.


Kellogg S. Stelle (1977)

Renormalization of higher--derivative gravity.

Phys. Rev. D 16, 953-969.


Proves the renormalizability of gravity in the presence of curvature squared terms. The analysis is done in flat space, assuming that the cosmological constant is zero.


R.E. Kallosh, O.V. Tarasov, I.V. Tyutin (1978)

One Loop Finiteness Of Quantum Gravity Off Mass Shell.

Nucl. Phys. B137, 145-163

It is observed that the divergences that vanish on shell depend on the gauge parameters and can be made to vanish by suitable choices of gauge parameters. This logic is applied to the ‘t Hooft Veltman one loop divergences.


B.L. Voronov, I.V. Tyutin (1984)

On Renormalization Of R**2 Gravitation. (In Russian).

Yad.Fiz.39, 998-1010


E. Tomboulis (1977)

1/N expansion and renormalizability in quantum gravity

Phys. Lett. 70 B, 361.


E. Tomboulis (1980).

Renormalizability and asymptotic freedom in quantum gravity. 

Phys. Lett. B 97, 77.

These two papers discuss the 1/N approximation in gravity, where N is the number of matter fields.


Marc H. Goroff, Augusto Sagnotti (1986)

The Ultraviolet Behavior of Einstein Gravity.

Nucl. Phys. B266 709

It was shown here that in pure gravity there is a two loop logarithmic divergence proportional to the third power of the Weyl tensor, and hence that the theory is perturbatively nonrenormalizable.


Anton E.M. van de Ven (1992)

Two loop quantum gravity.

Nucl. Phys. B378, 309-366

Repeats the calculation of Goroff and Sagnotti 1986 using heat kernel methods.

J. Julve, M. Tonin (1982)

Quantum Gravity with Higher Derivative Terms.

Nuovo Cim. B46, 137-152

Computes the beta functions of higher derivative gravity. The contribution of the “third ghost” is not taken into account.


Efim S. Fradkin and Arkady A. Tseytlin (1981)

Renormalizable Asymptotically Free Quantum Theory Of Gravity.

Phys.Lett. B104, 377-381


Efim S. Fradkin and Arkady A. Tseytlin (1982)

Higher Derivative Quantum Gravity: One Loop Counterterms and Asymptotic Freedom.

Nucl. Phys. B 201, 469.

In these two papers the beta functions of higher derivative gravity are calculated. The contribution of the “third ghost”, is taken into account. It is conjectured that gravity makes matter interactions asymptotically free.

I.G. Avramidy and A.O. Barvinsky (1985)

Asymptotic freedom in higher--derivative quantum gravity.

Phys. Lett. 159B, 269

This paper rederives the results of Fradkin and Tseytlin 1982 correcting a numerical mistake. It establishes the correct beta functions and asymptotic freedom for the dimensionless coefficients of the curvature squared terms. (There are two such couplings, because total derivatives are neglected).

Guilherme de Berredo--Peixoto and Ilya L. Shapiro (2004)

Conformal quantum gravity with the Gauss-Bonnet term.

Phys.Rev.D70, 044024


Guilherme de Berredo--Peixoto and Ilya L. Shapiro (2005)

Higher derivative quantum gravity with Gauss - Bonnet term.

Phys. Rev. D 71, 064005.


Extends the results of Avramidy and Barvinsky 1985. The beta functions of higher derivative gravity are calculated around four dimensions, including the Gauss-Bonnet term (which is topological in d=4).

A.V. Smilga (2005)

Benign versus malicious ghosts in higher derivative gravity
Nucl. Phys. B 706 (2005) 598


A.V. Smilga (2006)

Ghost-free higher derivative theory
Phys. Lett. B 632 (2006) 433


B. Holdom and J. Ren (2015)

QCD analogy for quantum gravity
Phys. Rev. D93 (2016) 124030

arXiv:1512.05305 [hep-th]

John F. Donoghue (2016a)

Is the spin connection confined or condensed?

arXiv:1609.03523 [hep-th]

John F. Donoghue (2016b)

A conformal model of gravitons

arXiv:1609.03524 [hep-th]

John F. Donoghue (2017)

Quartic propagators, negative norms and the physical spectrum

arXiv:1704.01533 [hep-th]

Euclidean quantum gravity

S.W. Hawking (1977)

Zeta Function Regularization of Path Integrals in Curved Space-Time.

Commun. Math. Phys. 55, 133

A famous paper on applications of zeta function and heat kernel techniques to quantum fields in curved spacetime.

S.W. Hawking (1978a)

Space-Time Foam.

Nucl. Phys. B144, 349-362

S.W. Hawking (1978b)

Euclidean Quantum Gravity.

Cargese Summer Inst. 1978, 0145

Lectures presented at 1978 Cargese Summer School, Cargese, France, Jul 10-29, 1978.

G.W. Gibbons, M.J. Perry (1978)

Quantizing Gravitational Instantons.

Nucl. Phys. B146, 90

G.W. Gibbons, S.W. Hawking, M.J. Perry (1978)

Path Integrals and the Indefiniteness of the Gravitational Action.

Nucl. Phys. B138, 141

It is proposed here that to avoid the unboundedness from below of the Hilbert action, the path integration over conformal factors should be rotated in the imaginary plane.

S.W. Hawking, Don N. Page, C.N. Pope (1979)

The Propagation Of Particles In Space-Time Foam.

Phys. Lett. B86, 175-178

S.M. Christensen, M.J. Duff (1979)

New Gravitational Index Theorems and Supertheorems.

Nucl. Phys. B154:301

S.M. Christensen, M.J. Duff (1980)

Quantizing Gravity with a Cosmological Constant.

Nucl. Phys. B170, 480

Zeta function calculation of one loop effective action for gravity with cosmological constant.

H. Lu and C. Pope
Critical gravity in four dimensions
Phys.Rev.Lett. 106 (2011) 181302

arXiv:1101.1971 [hep-th]

Effective field theory of gravity

John F. Donoghue (1994a)

Leading quantum correction to the Newtonian potential.

Phys. Rev. Lett. 72, 2996 (1994)


John F. Donoghue (1994b)

General Relativity as an effective field theory: The leading quantum corrections.

Phys. Rev. D 50, 3874 (1994)


The leading quantum corrections to the Newtonian potential between two heavy particles corresponds to non-analytic (more precisely, logarithmic) terms in the scattering amplitude. In these seminal papers, it is suggested that these corrections can be calculated using effective field theory methods and that they are independent of any regularization and renormalization ambiguity. For this calculation only one particle reducible diagrams are retained, i.e. the vacuum polarization and vertex corrections. Some of the vertex corrections are incorrectly evaluated.

H.W. Hamber and Liu (1995)

On the quantum corrections to the Newtonian potential.

Phys. Lett. B357, 51


The main conceptual step forward in this paper is that one particle irreducible diagrams have also to be taken into account. The evaluation of the diagrams again contains mistakes.

A. Akhundov, S. Bellucci and A. Shiekh (1996)

Gravitational interaction to one loop in effective quantum gravity.

Phys. Lett. B395, 16-23 (1997)


In this paper the one particle reducible potential is evaluated. The results for the vertex corrections are different from Donoghue's.

John F. Donoghue (1995)

Introduction to the effective field theory description of gravity.


Talk given at Advanced School on Effective Theories, Almunecar, Spain, 25 Jun - 1 Jul 1995.

N.E.J. Bjerrum-Bohr (2002)

Leading quantum gravitational corrections to scalar QED.

Phys. Rev. D66, 084023


I.B. Khriplovich, G.G. Kirilin (2002)

Quantum power correction to the Newton law.

J. Exp. Theor. Phys. 95, 981-986 (Zh. Eksp. Teor. Fiz. 95, 1139-1145 (2002))


This paper points out numerical errors in previous calculations. However, the triangle vertex correction is still not correctly evaluated.

Niels Emil Jannik Bjerrum-Bohr , John F. Donoghue, Barry R. Holstein (2003a)

Quantum corrections to the Schwarzschild and Kerr metrics.

Phys. Rev. D68, 084005; Erratum-ibid.D71, 069904 (2005)


In this paper a class of diagrams that contribute to the gravitational scattering of two particles is interpreted as a dependence of Newton’s constant on distance. The coefficient of the leading correction is such that gravity is antiscreening.

N.E.J. Bjerrum-Bohr, J.F. Donoghue and B.R. Holstein (2003b)

Quantum gravitational corrections to the nonrelativistic scattering potential of two masses.

Phys. Rev. D 67, 084033

[Erratum-ibid. D 71 (2005) 069903


This paper contains the "definitive” result for the leading classical and quantum corrections to Newton’s potential, as obtained from the full scattering amplitude. It agrees with the results of I.B. Khriplovich, G.G. Kirilin (2004)

Cliff P. Burgess (2004)

Quantum Gravity in Everyday Life: General Relativity as an Effective Field Theory


A review of gravity as an effective quantum field theory. Detailed discussion of estimates for the size of quantum corrections to scattering amplitudes.

I.B. Khriplovich, G.G. Kirilin (2004)

Quantum long range interactions in general relativity.

J. Exp. Theor. Phys. 98, 1063-1072


In the proceedings of 5th International Conference on Symmetry in Nonlinear Mathematical Physics (SYMMETRY 03), Kiev, Ukraine, 23-29 June 2003.

G.G. Kirilin (2007)

Quantum corrections to the Schwarzschild metric and reparametrization transformations.

Phys. Rev. D75, 108501


Criticizes the results of Bjerrum-Bohr , Donoghue and Holstein (2003a) for lack of reparametrization invariance.

N.E.J. Bjerrum-Bohr, J.F. Donoghue and B.R. Holstein (2007)

On the parameterization dependence of the energy momentum tensor and the metric.

Phys. Rev. D75, 108502


A detailed reply to the criticism in Kirilin (2007)

D. Espriu and D. Puigdomenech (2009)

Gravity as an effective field theory


Lectures given at the 49th Cracow School on Theoretical Physics, to appear in Acta Physica Polonica.

D. A. Satz, A. Codello and F. Mazzitelli (2010)

Low energy quantum Gravity from the Effective Average Action
Phys. Rev. D82, 084011 (2010)


A one loop calculation of the effective action of gravity based on solving the FRGE.
Takes into account terms quadratic in curvature, with a general form factor. The corrections to the Newtonian potential are computed and match with those calculated previously by taking into account graviton vacuum polarization effects.

S. Park and R.P. Woodard (2010)

Solving the Effective Field Equations for the Newtonian Potential
Class. and Quantum Grav. 27, 2450008 (2010)


A calculation of the quantum corrected Newtonian potential starting from the quantum field equations.

John F. Donoghue (2012)

The effective field theory treatment of quantum gravity

AIP Conf. Proc. 1483, 73-94 (2012)

arXiv:1209.3511 [gr-qc]

Presented at the Sixth International School on Field Theory and Gravitation, Petropolis, Brazil, April 2012

John F. Donoghue (2016a)

Is the spin connection confined or condensed?

arXiv:1609.03523 [hep-th]

John F. Donoghue (2016b)

A conformal model of gravitons

arXiv:1609.03524 [hep-th]

John F. Donoghue, Mikhail.M. Ivanov and Andrey Shkerin (2017a)

EPFL Lectures on General Relativity as a Quantum Field Theory

arXiv:1702.00319 [hep-th]

John F. Donoghue (2017b)

Quartic propagators, negative norms and the physical spectrum

arXiv:1704.01533 [hep-th]

Discrete gravity

Herbert W. Hamber, Ruth M. Williams (1995)

Newtonian potential in quantum Regge gravity.

Nucl. Phys. B435, 361-398


Herbert W. Hamber (2000)

Gravitational scaling dimensions,

Phys. Rev. D 61, 124008.

Herbert W. Hamber and Ruth M. Williams (2004)

Non--perturbative gravity and the spin of the lattice graviton.

Phys. Rev. D 70, 124007.


Herbert W. Hamber, Ruth M. Williams (2005)

Nonlocal effective gravitational field equations and the running of Newton's G.

Phys. Rev.D72, 044026


Herbert W. Hamber, Ruth M. Williams (2006)

Nonlocal effective field equations for quantum cosmology.

Mod. Phys. Lett. A21, 735-742


Herbert W. Hamber, Ruth M. Williams (2007)

Renormalization group running of Newton's G: The Static isotropic case.

Phys. Rev. D75, 084014


Jan Ambjørn, Jerzy Jurkiewicz and Renate Loll (2000).

A Nonperturbative Lorentzian path integral for gravity

Phys. Rev. Lett. 85, 924-927


Jan Ambjørn, Jerzy Jurkiewicz and Renate Loll (2001)

Dynamically triangulating Lorentzian quantum gravity.

Nucl. Phys. B610, 347-382


Jan Ambjørn, Jerzy Jurkiewicz and Renate Loll (2004)

Emergence of a 4-D world from causal quantum gravity

Phys. Rev. Lett. 93 131301


Jan Ambjørn, Jerzy Jurkiewicz and Renate Loll (2005a)

Spectral dimension of the universe.

Phys. Rev. Lett. 95, 171301.


Study the diffusion of a point particle in a dynamically triangulated spacetime.

Jan Ambjørn, Jerzy Jurkiewicz and Renate Loll (2005b)

Reconstructing the universe.

Phys. Rev. D 72, 064014. 


A summary of results obtained in the Causal Dynamical Triangulation approach.

Renate Loll (2007)

The Emergence of spacetime or quantum gravity on your desktop.

arXiv:0711.0273 [gr-qc]

Plenary talk at GR18: 18th International Conference on General Relativity and Gravitation 7th Edoardo Amaldi Conference on Gravitational Waves Amaldi7), Sydney, Australia, 8-13 Jul 2007.

J. Ambjørn, A. Goerlich, J. Jurkiewicz, R. Loll  (2007)

Planckian Birth of the Quantum de Sitter Universe.

Phys. Rev. Lett. 100, 091304

arXiv:0712.2485 [hep-th]

J. Ambjørn, A. Goerlich, J. Jurkiewicz, R. Loll  (2008)

The Nonperturbative Quantum de Sitter Universe.

Phys. Rev. D78, 063544

arXiv:0807.4481 [hep-th]

J. Ambjørn, A. Goerlich, J. Jurkiewicz, R. Loll  (2010)

CDT-an entropic theory of quantum gravity.

arXiv:1007.2560 [hep-th]

Lectures presented at the "School on Non-Perturbative Methods in Quantum Field Theory" and the "Workshop on Continuum and Lattice Approaches to Quantum Gravity", Sussex, September 15th-19th 2008 . To appear as a contribution to a Springer Lecture Notes in Physics book.

J. Ambjørn, A. Goerlich, J. Jurkiewicz, R. Loll, J. Gizbert-Studnicki, T. Trzesniewski  (2011)

The semiclassical limit of causal dynamical triangulations.
Nucl. Phys. B894, 144-165 (2011)

arXiv:1102.3929 [hep-th]

J. Laiho and D. Coumbe  (2011)

Evidence for asymptotic safety from lattice quantum gravity.

arXiv:1104.5505 [hep-lat]

A numerical evaluation suggesting that the spectral dimension of spacetime at short distances is equal to 3/2. It is argued that this may resolve the tension between asymptotic safety and the holographic principle.

Rajesh Kommu  (2011)

A validation of Causal Dynamical Triangulations.

arXiv:1110.6875 [gr-qc]

An independent numerical verification of the results by the group of Ambjørn, Jurkiewicz and Loll.

Astrid Eichhorn and Tim Koslowski  (2013)

Continuum limit in matrix models for quantum gravity from the functional renormalization group.

arXiv:1309.1690 [hep-th]

An application of the Wetterich equation to matrix models and tensor models.

Astrid Eichhorn and Tim Koslowski  (2017)

Flowing to the continuum in discrete tensor models for quantum gravity

arXiv:1701.03029 [gr-qc]

Astrid Eichhorn  (2017)

Towards coarse graining of discrete Lorentzian quantum gravity
Class.Quant.Grav. 35 (2018) no.4, 044001

arXiv:1709.10419 [gr-qc]

Astrid Eichhorn, Tim Koslowski, Antonio D. Pereira  (2018)

Status of background-independent coarse-graining in tensor models for quantum gravity

arXiv:1811.12909 [gr-qc]

Giuseppe Clemente, Massimo D'Elia, Alessandro Ferraro  (2019)

Spectral Methods and Running Scales in Causal Dynamical Triangulations

arXiv:1903.00430 [gr-qc]

Antonio D. Pereira  (2019)

Quantum spacetime and the renormalization group: Progress and visions

arXiv:1904.07042 [gr-qc]

Gravitational effects on matter couplings

L. Griguolo and R. Percacci (1995)

“The beta functions of a scalar theory coupled to gravity”,

Phys. Rev.  D 52, 5787 (1995).

arXiv: hep-th/9504092

S.P. Robinson and F. Wilczek (2005)

Gravitational corrections to running gauge couplings.

Phys. Rev. Lett. 96, 231601


Compute the effect of gravity (treated as an effective field theory) on the running of the gauge coupling.

Artur R. Pietrykowski (2007)

Gauge dependence of gravitational correction to running of gauge couplings.

Phys. Rev. Lett. 98, 061801


Notes that the results of Robinson and Wilczek (2005) are gauge-dependent.

David J. Toms (2007)

Quantum gravity and charge renormalization.

Phys. Rev. D76, 045015

arXiv:0708.2990 [hep-th]

Finds a vanishing gravitational correction to the Yang-Mills beta function. Dimensional regularization is used.

Dietmar Ebert, Jan Plefka, Andreas Rodigast (2007)

Absence of gravitational contributions to the running Yang-Mills coupling.

Phys. Lett. B660, 579-582 (2008).

arXiv:0710.1002 [hep-th]

Also finds a vanishing gravitational correction to the Yang-Mills beta function.

Yong Tang, Yue-Liang Wu (2008)

Gravitational Contributions to the Running of Gauge Couplings.
Commun. Theor. Phys. 54, 1040 (2010)

arXiv:0807.0331 [hep-ph]

These authors use a regularization method that preserves gauge invariance while not
automatically discarding the quadratic divergences, and find that the gravitational corrections to the running gauge couplings is nonzero and consistent with the Robinson-Wilczek result.

David J. Toms (2008)

Cosmological constant and quantum gravitational corrections to the running fine structure constant.

Phys. Rev. Lett. 101. 131301

arXiv:0809.3897 [hep-th]

Takes into account the effect of the cosmological constant on the running of the electric charge.

Xavier Calmet, Stephen D.H. Hsu, David Reeb (2008)

Grand unification and enhanced quantum gravitational effects.

Phys. Rev. Lett. 101, 171802

arXiv:0805.0145 [hep-ph]

It is shown that in GUT models with large representations the gravitational effects can be quite sizable,
in fact they can be even more important than two loop effects that are usually taken into account in discussions on the unification of couplings.

Xavier Calmet, Stephen D.H. Hsu, David Reeb (2009)

Grand unification through gravitational effects.
Phys. Rev. D81, 035007 (2010)

arXiv:0911.0415 [hep-ph]

Zanusso, L. Zambelli, G.P. Vacca and R. Percacci (2009)

Gravitational corrections to Yukawa systems.

Phys. Lett. B689 90-94 (2010)

arXiv:0904.0938 [hep-th]

Compute the effect of gravity, described by the Einstein-Hilbert action, on the running of the Yukawa coupling and scalar potential.

Andreas Rodigast and Theodor Schuster (2009)

Gravitational corrections to Yukawa and Φ4 interactions.
Phys. Rev. Lett. 104, 081301 (2010)

arXiv:0908.2422 [hep-th]

Compute the effect of gravity, described by the Einstein-Hilbert action, on the running of the Yukawa coupling and scalar potential. Since they use dimensional regularization, an effect is only found in the presence of masses.

J.E. Daum, U. Harst and M. Reuter (2009)

Running gauge coupling in asymptotically safe quantum gravity
JHEP 1001, 084 (2010)

arXiv:0910.4938 [hep-th]

Applying the functional RG flow equation in background Yang-Mills and gravitational gauges with gauge parameters a=1, a nonvanishing gravitational correction to the YM beta function is found.

J.E. Daum, U. Harst and M. Reuter (2010)

Non-perturbative QEG corrections to the Yang-Mills beta function

arXiv:1005.1488 [hep-th]

To appear in the proceedings of 9th Hellenic School and Workshops on Elementary Particle Physics and Gravity (CORFU 2009), Corfu, Greece, 30 Aug - 20 Sep 2009.

Hong-Juan He, Xu-Feng Wang and Zhong-Zhi Xianyu (2010)

Gauge-Invariant Quantum Gravity Corrections to Gauge Couplings via Vilkovisky-DeWitt Method and Gravity Assisted Gauge Unification.

arXiv:1008.1839 [hep-th]

Compute the one loop beta function with the Vilkovisky-de Witt method and find a nontrivial gravitational correction, making gauge fields asymptotically free, both for abelian and nonabelian gauge fields. Same calculation for scalar self interaction gives positive correction to beta function, in accordance with earlier results.

O. Zanusso, G.P. Vacca (2010)

Asymptotic safety in Einstein gravity and scalar-fermion matter.

Phys. Rev. Lett.  105, 231601 (2010)

arXiv:1009.1735 [hep-th]

Extend the earlier result by Zanusso, Zambelli, Vacca, Percacci by including the effect of the running of the gravitational couplings, and the anomalous dimensions of the scalars and fermions.

David J. Toms (2010)

Quantum gravitational corrections to quantum electrodynamics

Nature 468, 56-59 (2010)

arXiv:1010.0793 [hep-th]

Computes the divergent part of the Vilkovisky-de Witt effective action of QED coupled to gravity. Quadratic divergences are found. Gravity gives a negative contribution to the QED beta function.

Mohamed M. Anber, John F. Donoghue and Mohamed El-Houssieny (2010)

Running couplings and operator mixing in the gravitational corrections to coupling constants.

Phys. Rev. D83, 124003 (2011)

arXiv:1011.3229 [hep-th]

The authors discuss physical processes involving scalar and Yukawa couplings in the presence of gravity, in perturbation theory. They show that quantum effects cannot be universally absorbed in redefinitions of the couplings, making the definition of the gravitational contributions to the matter beta functions ambiguous and not very useful. The authors conclude that the gravitational loop effects should be described instead by higher dimension operators in the effective theory.

John Ellis and Nick E. Mavromatos (2010)

On the interpretation of gravitational corrections to gauge couplings.

arXiv:1012.4353 [hep-th]

It is pointed out that the gravitational correction to gauge couplings is sensitive to field redefinitions. This is along the same line as the preceding paper.

Sarah Folkerts, Daniel Litim and Jan Pawlowski (2011)

Asymptotic freedom of Yang-Mills theory with gravity.
Phys. Lett. B709, 234-241 (2012)

arXiv:1101.5552 [hep-th]

The authors first use functional RG and the background field method to calculate the beta functions in a gauge theory coupled to gravity and exhibit a specific choice of cutoff such that at one loop the gauge and gravitational couplings evolve separately. There is therefore no gravitational contribution to the gauge beta function at one loop. They then argue that this background field calculation contains unphysical contributions from the background field dependence of the cutoff, and that the physical part of the beta function would contain a nonvanishing gravitational contribution. They then perform another calculation with trivial flat backgrounds, and a different tensor structure for the cutoff. They show in general that the gravitational contribution is scheme dependent, but always consistent with asymptotic freedom, both in one loop approximation and also for large gravitational anomalous dimension. The gravitational contribution vanishes whenever the cutoff satisfies a certain kinematical identity.

U. Harst and M. Reuter (2011)

QED coupled to QEG
JHEP 1105, 119 (2011)

arXiv:1101.6007 [hep-th]

Here it is pointed out that the coupled system gravity+QED has, in addition to the Gaussian fixed point, two others: a "Gaussian matter" fixed point where QED is asymptotically free but gravity is interacting, and another where both gravity and QED are interacting. The latter has a lower dimensional critical surface and is therefore more predictive. One can use this fixed point to predict the value of the fine structure constant.

J.C.C. Felipe, L.C.T. Brito, M. Sampaio and M.C. Nemes (2011)

Quantum gravitational contributions to the beta function of quantum electrodynamics.
Phys. Lett. B700, 86-89 (2011)

arXiv:1103.5824 [hep-th]

A perturbative evaluation of the quadratic divergences due to gravity, emphasizing the source of ambiguities.

Andreas Rodigast and Theodor Schuster (2011)

Gravitational corrections to non gauge interactions.
Nucl. Phys. Proc. Suppl. 216, 263-264 (2011)

Proceedings of "String Theory: Formal Developments And Applications" 21 Jun - 3 Jul 2010, Cargese, France

Mohamed M. Anber, John F. Donoghue (2011)

On the running of the gravitational constant

arXiv:1111.2875 [hep-ph]

By considering several examples of scattering processes in the perturbative (effective field theory) regime of gravity, the authors argue that there is no universal and useful definition of a running Newton's constant, since quantum effects are described instead by the appearance of other operators in the effective Lagrangian. Possible issues in the asymptotic safety program are pointed out.

J.C.C. Felipe, L.A. Cabral, L.C.T. Brito, M. Sampaio and M.C. Nemes (2011)

Ambiguities in the gravitational correction of quantum electrodynamics.

arXiv:1205.6779 [hep-th]

Hao-Ran Chang, Wen-Tao Hou and Yi Sun (2012)

Gravitational corrections to phi^4 theory with spontaneously broken symmetry

arXiv:1207.5981 [hep-th]

Artur R. Pietrykowski (2012)

Interacting scalar fields in the context of effective quantum gravity

arXiv:1210.0507 [hep-th]

This paper analyzes the effect of gravitational interactions on a scalar field with analytic potential, in view of possible solutions of the problem of triviality. The scalar effective action is computed including terms up to two derivatives, also correcting some misprint in
A.O. Barvinsky, A.Yu. Kamenshchik, I.P. Karmazin (1993).

G. Narain and R. Anishetty (2012)

Charge renormalization due to graviton loops

JHEP 1307 (2013) 106

arXiv:1211.5040 [hep-th]

G. Narain and R. Anishetty (2013)

Running couplings in quantum theory of gravity coupled to gauge fields

JHEP 1310 (2013) 203

arXiv:1309.0473 [hep-th]

S. Gonzales-Martin and C.P. Martin (2017)

Do the gravitational corrections to the beta functions of the quartic and Yukawa couplings have an intrinsic physical meaning?

arXiv:1707.06667 [hep-th]

The authors calculate the gravitational correction to the beta functions of scalar and Yukawa couplings both in GR and in unimodular gravity