Steven Weinberg (1976)
Critical Phenomena for Field Theorists.
presented at Int. School of Subnuclear Physics, Ettore
Majorana, Erice, Sicily, Jul 23 -
Aug 8, 1976.
Published in Erice Subnucl. Phys.1976:1
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
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
I. Jack, D.R.T. Jones (1991)
The Epsilon expansion of two-dimensional quantum gravity.
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.
series of papers elaborate on the issues raised in Kawai and
Martin Reuter (1996)
Nonperturbative evolution equation for quantum gravity.
Phys. Rev. D57, 971.
this paper the ERGE is written for gravity. It is then
truncated and the beta functions for
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
using the ERGE, the effect of an R2 term on the
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.
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.arXiv:gr-qc/0006008
Martin Reuter (2000)
Annual Report 2000 of the International School in Physics and Mathematics, Tbilisi, Georgia.
Oliver Lauscher and Martin Reuter (2001)
Ultraviolet fixed point and generalized flow equation of quantum gravity.
Phys. Rev. D65, 025013.
flow equation is analyzed using the
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.
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
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.
means of a clever choice of cutoff function, closed
expressions are given for the beta functions of the
cosmological constant and
Roberto Percacci and Daniele Perini (2004)
On the ultraviolet behaviour of Newton's constant.
Class. and Quantum Grav. 21, 5035.
paper discusses an apparent puzzle in asymptotically safe
gravity. It is noted that
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.
“Quantum gravity” , ed. B. Fauser, J. Tolksdorf and
talk at 14th
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.
Conf. Proc. 841, 322-329 (2006).
Also in *Oviedo
presented at 28th Spanish Relativity Meeting (ERE05): A
Century of Relativity Physics,
Peter Fischer, Daniel F. Litim (2006)
Fixed points of quantum gravity in higher dimensions.
Conf. Proc. 861, 336-343 (2006).
Also in *Paris 2005, Albert Einstein's century* 336-343
presented at Albert Einstein's Century International
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
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
terms with up to four derivatives of the metric. The old
results are reproduced for the dimensionless couplings,
but in the case of
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
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.
Lectures given at First Quantum Geometry and Quantum Gravity School, Zakopane, Poland, 23 Mar - 3 Apr 2007.
Roberto Percacci (2007)
'Approaches to Quantum Gravity: Toward a New Understanding
of Space, Time and Matter' ed. D. Oriti,
Pedro F. Machado and Frank Saueressig (2007)
On the renormalization group flow of f(R)-gravity.
Phys. Rev. D77, 124045
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)
independence and asymptotic safety in conformally reduced
Phys. Rev. D79, 105005 (2009)
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
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.
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)
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
Elisa Manrique and Martin Reuter (2008)
Bare Action and Regularized Functional Integral of Asymptotically Safe Quantum Gravity
Phys. Rev. D79, 025008 (2009).
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
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).
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.
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)
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
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)
vs. Effective Fixed Point Action in Asymptotic Safety: The
PoS CLAQG08 (2011)
given by M.R. at the Workshop on Continuum and Lattice
Approaches to Quantum Gravity. Sept. 2008, Brighton
Astrid Eichhorn, Holger Gies, Michael M. Scherer (2009)
Asymptotically free scalar curvature-ghost coupling in Quantum Einstein Gravity.
Phys. Rev. D80, 104003 (2009)
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)
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)
Field Theory, Past and Future.
PoS CD09, 001 (2009)
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
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.
Gaurav Narain and Roberto Percacci (2009b)Renormalization group flow in scalar-tensor theories I.
Gaurav Narain and Christoph Rahmede (2009)Renormalization group flow in scalar-tensor theories II.
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
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).
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)
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).
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)
induced bimetric actions for gravity.
Ann. Phys. 326, 440-462 (2011)
Here the flow of bimetric actions is calculated in the large N limit.
Elisa Manrique, Martin Reuter and Frank Saueressig (2010b)
Renormalization Group Flows in Quantum Einstein Gravity.
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)
safety, emergence and minimal length
Class. and Quantum Grav. 27, 245026
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.
Ghosts and stability of asymptotically safe gravity in the Minkowski background.
Dario Benedetti, Kai Groh, Pedro F. Machado and Frank Saueressig (2010)
universal RG machine
JHEP 1106, 079 (2011)
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
Jan-Erik Daum and Martin Reuter (2010a)
group flow of the Holst action
Phys.Lett. B710 (2012) 215-218
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)
Immirzi parameter and asymptotic safety
PoS 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)
Elisa Manrique, Stefan Rechenberger and Frank Saueressig (2010)
safe Lorentzian gravity
Phys. Rev. Lett. 106 251302 (2011)
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)
RG flow equation: regularization and coarse-graining in
Phys. Rev. D83 125024 (2011)
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)
quantum gravity with the Immirzi parameter.
JHEP 1106, 107 (2011)
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)
fermions in quantum gravity.
New J. of Phys. 13, 125012 (2011)
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)
safety goes on shell
New J. of Phys. 14, 015005 (2012)
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?
Alessandro Codello (2011)
Large N quantum gravity
New J. of Phys. 14, 015009 (2012)
Astrid Eichhorn (2011)
consequences of quantum gravity: can light fermions exist?
J. Phys. Conf. Ser. 360, 012057 (2012)
Talk given at Loops'11, Madrid, to appear in J. of Phys. Conf Ser.
Martin Reuter and Frank Saueressig (2011)
space-times under the microscope: a renormalization group
view of Monte Carlo data
JHEP 1112, 012 (2011)
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.
In the proceedings of the conference "Time and matter" Budva, Montenegro, October 2010.
Roberto Percacci (2011b)
flow of Weyl-invariant dilaton gravity.
New J. of Phys. 13, 125013 (2011)
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)
derivative gravity from the universal renormalization group
PoS EPS-HEP 2011 124 (2011)
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)
heat kernel expansion and its application to fields with
Martin Reuter and Frank Saueressig (2012a)
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
The "tetrad only" theory space: nonperturbative
renormalization flow and asymptotic safety
JHEP 1205 (2012) 005
The phase diagram of quantum gravity from
diffeomorphism invariant RG flows
Astrid Eichhorn (2012)
gravity-induced matter self-interactions in the asymptotic
Phys. Rev. D86, 105021 (2012)
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
S. Nagy, J. Krizsan and K. Sailer (2012)
fixed point in quantum Einstein gravity
JHEP 1207 (2012) 102
Dario Benedetti and Francesco Caravelli (2012)
local potential approximation in quantum gravity
JHEP 1206 (2012) 017, Erratum-ibid. 1210 (2012) 157
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)
function and asymptotic safety in three dimensional higher
Class.Quant.Grav. 29 (2012) 205012
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
Limit cycles and quantum gravity
Martin Reuter and Frank Saueressig (2012b)
safety, fractals and cosmology
given at the Sixth Aegean Summer School on Quantum Gravity and
Quantum Cosmology, Naxos, Greece, september 2011.
Stefan Rechenberger and Frank Saueressig (2012)
R^2 phase diagram of QEG and its spectral dimension
Phys.Rev. D86 (2012) 024018
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
Rev. D 86, 105027 (2012)
Andreas Nink and Martin Reuter (2012)
the physical mechanism underlying asymptotic safety
JHEP 1301 (2013) 062
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)
of three-dimensional Quantum Einstein Gravity
JHEP 1211 (2012) 131
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
Nicolai Christiansen, Daniel Litim, Jan Pawlowski and Andreas Rodigast (2012)
points and infrared completion of quantum gravity
Phys.Lett. B728 (2014) 114-117
Roberto Percacci and Pietro Dona' (2012)
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.
Astrid Eichhorn (2012)
Experimentally testing asymptotically safe quantum gravity with photon-photon scattering
Talk given at the 13th Marcel Grossmann meeting (Stockholm, july 2013)
Alessandro Codello, Giulio d'Odorico, Carlo Pagani and Roberto Percacci (2012)
group and Weyl invariance.
Class.Quant.Grav. 30 (2013) 115015
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)
on renormalization and asymptotic safety
Ann. Phys. (2013) 310-346
Juergen A. Dietz and Tim R. Morris (2012)
safety in the f(R) approximation
JHEP 1301 (2013) 108
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.
Asymptotic safety and black hole thermodynamics
Andreas Nink and Martin Reuter (2012)
quantum gravity, asymptotic safety and paramagnetic dominance
Astrid Eichhorn (2013b)
unimodular quantum gravity
Class.Quant.Grav. 30 (2013) 115016
Astrid Eichhorn (2013a)
ghosts in quantum gravity beyond perturbation theory
and Quantum Grav. 30, 115016 (2013)
Stefan Rechenberger and Frank Saueressig (2012)
functional renormalization group equation for foliated
JHEP 1303 (2013) 010
Dario Benedetti (2013)
On the number of relevant operators in asymptotically safe gravity
Europhys.Lett. 102 (2013) 20007
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)
bootstrap towards asymptotic safety
Jan-Eric Daum, Martin Reuter (2013)
gravity, asymptotic safety and the running Immirzi parameter
Annals Phys. 334 (2013) 351-419
A detailed account of the calculations in Daum and Reuter (2010a).
R. Percacci, C. Pope, M. Perry and E. Sezgin (2013)
functions of topologically massive supergravity
JHEP 1403 (2014) 083
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)
ground state of gravity theories with stabilized conformal
Phys. Rev. D.87, 084019
Alessandro Codello, Giulio d'Odorico, Carlo Pagani (2013)
closure of RG flow equations in quantum gravity
Phys.Rev. D89 (2014) 081701
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.
Probing the quantum nature of
spacetime by diffusion
Phys.Rev. D87 (2013) 12, 124028
Juergen A. Dietz and Tim R. Morris (2013)
operators in the exact renormalisation group and in the f(R)
approximation to asymptotic safety
JHEP 1307 (2013) 064
Nobuyoshi Ohta and Roberto Percacci (2013)
derivative gravity and asymptotic safety in diverse
Class.Quant.Grav. 31 (2014) 015024
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)
theory in the local potential approximation
New J.Phys. 16 (2014) 053051
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)
matters in asymptotically safe quantum gravity
Phys.Rev. D89 (2014) 084035
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)
and fixed points of non-integrable Weyl theory
Class. Quant. Grav. 31 (2014) 115005
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)
flows of Quantum Einstein Gravity on maximally symmetric
JHEP 1406 (2014) 026
study of the flow equation for conformally reduced f(R)
gravity in three dimensions. Two scaling solutions are
Nicolai Christiansen, Jan Pawlowski and Andreas Rodigast (2014)
flows in quantum gravity
Phys.Rev. D93 (2016) no.4, 044036
En route to background independence: broken
split-symmetry and how to restore it with bi-metric
Annals Phys. 350 (2014) 225-301
Propagating gravitons vs. dark matter in
asymptotically safe quantum gravity
JHEP 1412 (2014) 025
safety and the cosmological constant
JHEP 1601 (2016) 069
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)
of matter models with asymptotically safe quanum gravity
Canadian Journal of Physics, 2015, 93(9): 988-994
of Theory Canada 9.
K. Falls, D. Litim, K. Nikolakopulos and C. Rahmede (2013)
evidence for asymptotic safety of quantum gravity
Phys.Rev. D93 (2016) no.10, 104022
Ippocratis Saltas (2014)
On the UV structure of quantum unimodular gravity
parametrization dependence in asymptotically safe quantum
Phys.Rev. D91 (2015) 4, 044030
A new functional flow equation for
Einstein-Cartan quantum gravity
Annals Phys. 354 (2015) 637-704
Towards a C-function in quantum gravity
JHEP 1503 (2015) 065
Alessandro Codello, Giulio d'Odorico (2014)
and renormalization in two-dimensional quantum gravity
Phys.Rev. D92 (2015) 2, 024026
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)
flows of Quantum Einstein Gravity in the linear-geometric
Phys. 359 (2015) 141-165
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)
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)
the renormalization of Newton's constant
Phys.Rev. D92 (2015) no.12, 124057
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)
renormalization group flow of unimodular f(R) gravity
JHEP 1504 (2015) 096
flow equation for the function f is calculated in unimodular
gravity, using spectral sums. Approximate polynomial solutions
Julia Borchardt and Benjamin Knorr (2015)
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.
Is there a C-function in 4d quantum Einstein
Juergen A. Dietz and Tim R. Morris (2015)
exact renormalization group for conformally reduced gravity
JHEP 1504 (2015) 118
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)
proper fixed functional for four-dimensional Quantum Einstein
JHEP 1508 (2015) 113
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)
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.
and geodesics in the space of metrics
Phys.Rev. D92 (2015) no.10, 104013
Nicolai Christiansen, Benjamin Knorr, Jan Meibohm, Jan Pawlowski and M. Reichert (2015)
Phys.Rev. D92 (2015) no.12, 121501
Nobuyoshi Ohta, Roberto Percacci and Gian Paolo Vacca (2015a)
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
Holger Gies, Benjamin Knorr and Stefan Lippoldt (2015)
Parametrization Dependence in Quantum Gravity
Phys.Rev. D92 (2015) no.8, 084020
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
The metric on field space, functional
renormalization and metric-torsion quantum gravity
Ann. Phys. (2016)
Kin-ya Oda and Masatoshi Yamada (2016)
coupling in Higgs–Yukawa model with asymptotically safe
Class.Quant.Grav. 33 (2016) no.12, 125011
Jan Meibohm, Jan Pawlowski and M. Reichert (2015)
safety of gravity-matter systems
Phys.Rev. D93 (2016) no.8, 084035
On selfdual spin-connections and Asymptotic
Phys.Lett. B753 (2016) 395-400
Dario Benedetti (2015)Essential nature of Newton's constant in unimodular gravity
Nobuyoshi Ohta, Roberto Percacci and Gian Paolo Vacca (2015a)
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.
The unitary conformal field theory behind 2D
JHEP 1602 (2016) 167
Pietro Dona', Astrid Eichhorn, Peter Labus and Roberto Percacci (2015)
safety in an interacting system of gravity and scalar matter
Phys.Rev. D93 (2016) no.4, 044049
running Newton constant is derived from the graviton-scalar
three point function.
safe R+R^2 Gravity
Holger Gies, Benjamin Knorr, Stefan Lippoldt and Frank Saueressig (2016)The Gravitational Two-Loop Counterterm is Asymptotically Safe
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)
fermions in asymptotically safe quantum gravity
Eur.Phys.J. C76 (2016) no.5, 285
Tim R. Morris and Anthony W.H. Preston (2016)Manifestly diffeomorphism invariant classical Exact Renormalization Group
Peter Labus, Tim R. Morris and Zoe H. Slade (2016)Background independence in a background dependent renormalization group
Astrid Eichhorn, Aaron Held and Jan Pawlowski (2016)
gravity effects on a Higgs-Yukawa model
Phys.Rev. D94 (2016) no.10, 104027
Nobuyoshi Ohta, Roberto Percacci and Antonio Duarte Pereira (2016a)
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)
solutions for Dilaton Quantum Gravity
Phys.Lett. B769 (2017) 105-110
Jurgen Dietz, Tim R. Morris and Zoe H. Slade (2016)Fixed point structure of the conformal factor field in quantum gravity
Nobuyoshi Ohta and Kevin Falls (2016)
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.
gravity on foliated spacetime - asymptotically safe and
Phys.Rev. D95 (2017) no.8, 086013
Tim R. Morris (2016)Large curvature and background scale independence in single-metric approximations to asymptotic safety
Nobuyoshi Ohta, Roberto Percacci and Antonio Duarte Pereira (2016b)
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
Carlo Pagani and Martin Reuter (2016)Composite operators in asymptotic safety
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)
quantum gravity beyond perturbation theory
T. Denz, J. Pawlowski and M. Reichert (2016)
apparent convergence in asymptotically safe quantum gravity
Eur.Phys.J. C78 (2018) no.4, 336
Kevin Falls (2017)
renormalization schemes and asymptotic safety in quantum
Phys.Rev. D96 (2017) no.12, 126016
group fixed points of foliated gravity-matter systems
JHEP 1705 (2017) 093
Astrid Eichhorn and Nicolai Christiansen (2017)
asymptotically safe solution to the U(1) triviality problem
Phys.Lett. B770 (2017) 154-160
Yuta Hamada and Masatoshi Yamada (2017)Asymptotic safety of higher derivative quantum gravity non-minimally coupled with a matter system
Sergio Gonzales-Martin, Tim R. Morris and Zoe H. Slade (2017)Asymptotic solutions in asymptotic safety
W.B. Houthoff, A. Kurov and Frank Saueressig (2017)
of topology in foliated Quantum EInstein Gravity
scale-invariance in gauge-Yukawa systems compatible with the
Phys.Rev. D96 (2017) no.8, 084021
mass from asymptotic safety
Phys.Lett. B777 (2018) 217-221
Correlation functions on a curved background
S. Nagy, B. Fazekas, Z. Peli, K. Sailer and I. Steib (2017)
of fixed points in quantum Einstein gravity with R^2
Astrid Eichhorn (2017)Status of the asymptotic safety paradigm for quantum gravity and matter
bound on the abelian gauge coupling from asymptotic safety
JHEP 1801 (2018) 030
avoiding Ostrogradski instabilities within asymptotic safety
JHEP 1712 (2017) 121
renormalization group flows on
Found.Phys. 48 (2018) no.10, 1291-1304
Astrid Eichhorn, Stefan Lippoldt and Vedran Skrinjar (2017)Nonminimal hints for asymptotic safety
Nicolai Christiansen, Daniel F. Litim, Jan M. Pawlowski and Manuel Reichert (2017)
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
Benjamin Knorr (2017)
order quantum-gravitational correlations
Class.Quant.Grav. 35 (2018) no.11, 115005
Astrid Eichhorn, Aaron Held and Christof Wetterich (2017)Quantum gravity predictions for the fine-structure constant
Nicolai Christiansen, Kevin Falls, Jan Pawlowski and Manuel Reichert (2017)
dependence of quantum gravity
Phys.Rev. D97 (2018) no.4, 046007
Astrid Eichhorn, Yuta Hamada, Johannes Lumma and Masatoshi Yamada (2017)Quantum gravity fluctuations flatten the Planck-scale Higgs potential
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
Kevin Falls, Callum R. King, Daniel F. Litim Kostas Nikolakopoulos and Christoph Rahmede (2018)
safety of quantum gravity beyond Ricci scalars
Phys.Rev. D97 (2018) no.8, 086006
Tim R. Morris (2018)Renormalization group properties in the conformal sector: towards perturbatively renormalizable quantum gravity
Astrid Eichhorn, Aaron Held and Peter Vander Griend (2018)Asymptotic safety in the dark
Natalia Alkofer and Frank Saueressig (2018)Asymptotically safe f(R)-gravity coupled to matter I: the polynomial case
Bonanno, Alessia Platania and Frank Saueressig (2018)
bounds on the field content of asymptotically safe
Phys.Lett. B784 (2018) 229-236
Astrid Eichhorn, Peter Labus, Jan Pawlowski and Manuel Reichert (2018)Effective universality in quantum gravity
Matthew P. Kellett, Tim R. Morris (2018)Renormalization group properties of the conformal mode of a torus
Carlo Pagani and Martin Reuter (2018)Finite Entanglement Entropy in Asymptotically Safe Quantum Gravity
reconstructing the quantum effective action of gravity
Phys.Rev.Lett. 121 (2018) no.16, 161304
Gustavo Pazzini De Brito, Nobuyoshi Ohta, Antonio Duarte Pereira and Anderson Tomasz (2018)
Gabriele Gionti (2018)
Analysis of Asymptotically Safe Gravity
Natalia Alkofer (2018)Asymptotically safe f(R)-gravity coupled to matter II: global solutions
asymptotic safety scenario for quantum gravity – An appraisal
Simon Friederich (2018)
K. Falls, D. Litim, K. Nikolakopulos and J. Schroeder (2018)
of asymptotic safety for quantum gravity
Astrid Eichhorn, Stefan Lippoldt, Jan Pawlowski, Manuel Reichert and Marc Schiffer (2018)How perturbative is quantum gravity?
Astrid Eichhorn (2018)An asymptotically safe guide to quantum gravity and matter
Jan.M. Pawlowski, Manuel Reichert, Christof Wetterich, Masatoshi Yamada (2018)Higgs scalar potential in asymptotically safe quantum gravity
Gustavo P. De Brito, Yuta Hamada, Antonio D. Pereira, Masatoshi Yamada (2019)
Christof Wetterich (2019)Quantum scale symmetry
Christof Wetterich, Masatoshi Yamada (2019)Variable Planck mass from gauge invariant flow equation
Carlo Pagani, Martin Reuter (2019)
Background Independent Quantum Field Theory and Gravitating Vacuum Fluctuations
Phys. Rev. D60, 084011arXiv:1906.02507 [hep-th]
factors in asymptotic safety: conceptual ideas and
Class.Quant.Grav. 36 (2019) no.23, 234001
Senarath de Alwis, Astrid Eichhorn, Aaron Held, Jan Pawlowski, Marc Schiffer and Fleur Versteegen (2019)Asymptotic safety, string theory and the weak gravity conjecture
Gustavo P. De Brito, Astrid Eichhorn, Antonio D. Pereira (2019)A link that matters: towards phenomenological tests of unimodular asymptotic safety
John Donoghue (2019)
A critique of the asymptotic safety programarXiv: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.
paper discusses the geometry of a black hole taking into
account the RG flow of
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)
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)
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
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
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
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
scale dependence of
Daniel F. Litim and Tilman Plehn (2008)
Signatures of gravitational fixed points at the LHC.
Phys. Rev. Lett. 100, 131301
into account the asymptotically safe behaviour of
Daniel F. Litim and Tilman Plehn (2007)
Virtual gravitons at the LHC.
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)
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
Alfio Bonanno, Martin Reuter (2008)
Primordial Entropy Production and Lambda-driven Inflation from Quantum Einstein Gravity.
J. Phys. Conf. Ser.140, 012008
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)
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)
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)
Gravity Effects in the Kerr spacetime
Phys. Rev. D83, 044041 (2011)
Kevin Falls, Daniel F. Litim and Aarti Raghuraman (2010)
holes and asymptotically safe gravity
Int. J. Mod. Phys. A27 1250019 (2012)
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)
Safety, Asymptotic Darkness, and the hoop conjecture in the
Phys. Rev. D82, 124017 (2010)
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)
holes in an asymptotically safe gravity theory with higher
JCAP 1009, 002 (2010)
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)
asymptotically safe f(R) gravity
Class. and Quantum Grav. 28, 145026 (2011)
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
Roberto Casadio, Stephen Hsu and Behrouz Mirza (2010)
safety, singularities and gravitational collapse
Phys. Lett. B695, 317-319 (2011)
Sabine Hossenfelder and Roberto Percacci (2010)
special relativity and asymptotically safe gravity
Phys. Rev. D82, 124024
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)
on asymptotically safe inflation
Phys. Rev. D82, 127302 (2010)
scale cosmology and asymptotic safety in Resummed Quantum
PoS ICHEP 2010:477 (2010)
Gerwick, Daniel F. Litim and Tilman Plehn (2011)
safety and Kaluza-Klein gravitons at the LHC.
Phys. Rev. D83 084048 (2011)
Mark Hindmarsh, Daniel Litim and Christoph Rahmede (2011)
JCAP 1107, 019 (2011)
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)
asymptotic safety to dark energy
Phys. Lett. B704 10-14 (2011)
Rong-Jia Yang (2011)
Asymptotically safe phantom cosmology
Yi-Fu Cai and Damien Easson (2011)
safe gravity as a scalar-tensor theory and its cosmological
Phys. Rev. D84, 103502 (2011)
Adriano Contillo, Mark Hindmarsh and Christoph Rahmede (2011)
group improvement of scalar field inflation
Phys. Rev. D85, 043501 (2012)
Sungwook E. Hong, Young Jae Lee, Heeseung Zoe (2011)
Possibility of Inflation in Asymptotically Safe Gravity
Alfio Bonanno (2012)
effective action for asymptotically safe gravity
Phys.Rev. D85 (2012) 081503
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)
gravity from the renormalisation group
Phys.Rev. D86 (2012) 064029
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)
we see quantum gravity? Photons in the asymptotic-safety
JHEP 206, 156 (2012)
scattering is proposed as a possible experimental signature
of quantum gravitational effects in higher dimensional
Fedor Bezrukov, Mikhail. Yu. Kalmykov, Bernd A. Diehl and Mikhail Shaposhnikov (2012)
boson mass and new physics
JHEP 1210 (2012) 140
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)
safety, hypergeometric functions and the Higgs mass in
spectral action models
Int.J.Geom.Meth.Mod.Phys. 10 (2013) 1350036
antiscreening in perturbative quantum gravity and resolving
the Newtonian singularity
Chao Fang and Quin-Guo Huang (2012)
trouble with asymptotically safe inflation.
Kevin Falls and Daniel F. Litim (2012)
hole thermodynamics under the microscope
Phys.Rev. D89 (2014) 084002
Yi-Fu Cai, Yo-Chao Chang, Pisin Chen, Damien Easson and Taotao Qiu (2013)
constraints on Higgs modulated reheating of renormalization
group improved inflation
Phys.Rev. D88 (2013) 083508
T. Henz, J. Pawlowski, A. Rodigast and C. Wetterich (2013)
Dilaton quantum gravity
Edmund Copeland, Christoph Rahmede and Ippocratis Saltas (2013)
safe Starobinski inflation
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).
aspects of asymptotically safe black holes.
Class. and Quantum Grav. 31 (2013) 015006
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,
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.
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.
Koch, Carlos Contreras, Paola Rioseco and Frank Saueressig
holes and running couplings: a comparison of two
Springer Proc.Phys. 170 (2016) 263-269
of the Karl Schwarzschild meeting, Frankfurt am Main, July
Inflation, quintessence and the origin of mass
Nucl.Phys. B897 (2015) 111-178
Setting for Self-consistent Backgrounds
Phys.Rev. D91 (2015) no.2, 025009
Hole Solutions for Scale Dependent Couplings: The de Sitter
and the Reissner-Nordström Case
Class.Quant.Grav. 33 (2016) 035002
Georgios Kofinas, Vasilios Zarikas (2015)
of singularities in asymptotically safe Quantum Einstein
JCAP 1510 (2015) no.10, 069
Zhong-Zhi Xianyu and Hong-Jian He (2014)
Asymptotically safe Higgs inflationarXiv:1407.6993 [hep-ph.CO]
safe inflation from quadratic gravity
Phys.Lett. B750 (2015) 638-642
Georgios Kofinas, Vasilios Zarikas (2015)
Safe gravity and non-singular inflationary Big Bang with
Phys.Rev. D94 (2016) no.10, 103514
the Renormalization Scale in QFT
J.Phys.Conf.Ser. 720 (2016) no.1, 012020
K. Falls, D. Litim, K. Nikolakopulos and C. Rahmede (2016)
de Sitter solutions in asymptotically safe f(R) theories
Class.Quant.Grav. 35 (2018) no.13, 135006
Censorship in Quantum Einstein Gravity
Class.Quant.Grav. 34 (2017) no.9, 095012
Christof Wetterich and Masatoshi Yamada (2016)
hierarchy problem in asymptotically safe gravity - the
Phys.Lett. B770 (2017) 268-271
Alfio Bonanno and Frank Saueressig (2017)
safe cosmology - a status report
Comptes Rendus Physique 18 254-264
Safe gravitational collapse: Kuroda-Papapetrou RG-improved
PoS CORFU2016 (2017) 058
R. Moti, A. Shojai (2017)
the effect of renormalization group improvement on the
cosmological power spectrum
Eur.Phys.J. C78 (2018) no.1, 32
Ramon Torres (2017)
black holes, the cosmological constant, and asymptotic safety
Phys.Rev. D95 (2017) no.12, 124004
Georgios Kofinas, Vasilios Zarikas (2017)
solution of the dark energy and its coincidence problem
based on local antigravity sources without fine-tuning or
Phys. Rev. D 97, 123542 (2018)
Alfio Bonanno, Gabriele Gionti and Alessia Platania (2017)
and emergent cosmologies from ADM RG flows
Astrid Eichhorn, Aaron Held (2018)
difference for charged quarks from quantum gravity
Phys.Rev.Lett. 121 (2018) no.15, 151302
Astrid Eichhorn, Aaron Held and Christof Wetterich (2017)
predictions for the fine-structure constant
Phys.Lett. B782 (2018) 198-201
from star collapse, torsion and asymptotic safety of gravity
Yuexin Zhang, Menglei Zhou and Cosimo Bambi (2018)
line spectroscopy of black holes in asymptotically safe
Eur.Phys.J. C78 (2018) no.5, 376
in an effective gravitational model & asymptotic safety
Phys.Rev. D98 (2018) no.4, 043505
Giulia Gubitosi, Robin Ooijer, Chris Ripken, and Frank Saueressig (2018)
early and late time cosmology from the RG flow of gravity
the Asymptotically Safe Cosmology: cosmic acceleration
without dark energy
Giulia Gubitosi, Robin Oojer, Chris Ripken and Frank Saueressig (2018)
early and late time cosmology from the RG flow of gravity
JCAP 1812 (2018) no.12, 004
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)
Schwarzschild-(A)dS and Kerr-(A)dS spacetimes
Phys.Rev. D98 (2018) no.10, 106008
Vasilios Zarikas and Georgios Kofinas (2018)
and Phenomenological aspects of Asymptotic Safe Gravity
J.Phys.Conf.Ser. 1051 (2018) no.1, 012028
Ademola Adeifoba, Astrid Eichhorn and Alessia Platania (2018)
conditions for black-hole singularity-resolution in
asymptotically safe quantum gravity
safety and conformal standard model
Astrid Eichhorn, Stefan Lippoldt, Marc Schiffer (2018)
Zooming in on fermions and quantum gravityarXiv:1812.08782 [gr-qc]
and hierachies in asymptotically safe quantum gravity: a
Astrid Eichhorn, Marc Schiffer (2019)
d=4 as the critical dimensionality of asymptotically safe interactionsarXiv:1902.06479 [gr-qc]
Lando Bosma, Benjamin Knorr and Frank
Resolving Spacetime Singularities within Quantum Gravity
Aaron Held, Roman Gold, Astrid Eichhorn (2019)
Asymptotic safety casts its shadowarXiv:1904.07133 [gr-qc]
Alessia Platania (2019)
The inflationary mechanism in Asymptotically Safe GravityarXiv:1908.03897 [gr-qc]
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.
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
Alessandro Codello and Roberto Percacci (2008)
Fixed Points of Nonlinear Sigma Models in d>2.
Phys. Lett. B672, 280-283 (2009)
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.
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
Eur. Phys. J. C66, 403-418 (2010)
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
Acta Phys. Polon. supp. , 541 (2009)
A discussion of
the Gross-Neveu model using modern functional RG methods.
Talk presented at the Cracow School of Theoretical Physics, XLIX Course, Zakopane, Poland, May 31 - June 10, 2009.
Roberto Percacci and Omar Zanusso (2009)
One loop beta functions and fixed points in Higher Derivative Sigma Models
Phys. Rev. D81 065012 (2010)
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
Phys. Rev. D82, 085018, 2010
Asymptotic safety: a simple example.
Phys. Rev. D83, 085012 (2011)
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
Phys. Rev. D86, 105007, 2012
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
Phys. Rev. D83, 025016 (2011)
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)
Asymptotically safe weak interactions
Marco Fabbrichesi, Roberto Percacci, Alberto
Tonero and Luca Vecchi (2011)
The electroweak S and T parameters from a fixed
Phys. Rev. Lett. 107 021803 (2011)
Fermions and Goldstone bosons in an
asymptotically safe model
Daniel Litim, Roberto Percacci and Leslaw Rachwal (2011)
Scale-dependent Planck mass and Higgs VEV from
holography and functional renormalization
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
Holger Gies, Stefan Rechenberger, Michael Scherer and Luca Zambelli (2011)
asymptotic safety scenario for gauged chiral Higgs-Yukawa
Eur.Phys.J. C73 (2013) 2652
B. Wellegehausen, D. Koerner, A. Wipf (2014)
Asymptotic safety on the lattice: the O(N) sigma
D. Koerner, B. Wellegehausen, Andreas Wipf (2014)
MCRG flow for nonlinear sigma model
PoS LATTICE2013 (2013) 052
Daniel Litim and Francesco Sannino (2014)
JHEP 1412 (2014) 178
safe dark matter
Francesco Sannino and Ian M. Shoemaker (2014)
J. Kovacs, S. Nagy, and K. Sailer (2014)
Asymptotic safety in the sine-Gordon model
Daniel Litim and Francesco Sannino (2015)
stability of asymptotically safe gauge-Yukawa theories
JHEP 1601 (2016) 081
Holger Gies and Luca Zambelli (2015)
free scaling solutions in non-abelian Higgs models.
Niklas Gronlund Nielsen, Francesco Sannino and Ole Svendsen (2015)
from asymptotically safe theories
Phys.Rev. D91 (2015) 103521
Safety in the Conformal Hidden Sector?
J.Phys. G45 (2018) no.9, 095002
Andrew Bond and Daniel Litim (2016)
for asymptotic safety of gauge theories
Eur.Phys.J. C77 (2017) no.6, 429
Borut Bajc and Francesco Sannino (2016)
Asymptotically safe Grand UnificationarXiv:1610.09681 [hep-th]
Giulio Maria Pelaggi, Francesco Sannino,Alessandro Strumia, Elena Vigiani (2017)
Naturalness of Asymptotically safe HiggsarXiv:1701.01453 [hep-th]
Andrew Bond, Gudrun Hiller, Kamila Kowalska and Daniel Litim (2017)
for model building from asymptotic safety
JHEP 1708 (2017) 004
Steven Abel and Francesco Sannino (2017)
Radiative symmetry breaking from interacting UV fixed pointsarXiv:1704.00700 [hep-th]
Giulio Maria Pelaggi, Alexis D. Plascencia, Alberto Salvio, Francesco Sannino, Yuri Smirnov, Alessandro Strumia (2018)Asymptotically Safe Standard Model Extensions?
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 fermionsarXiv:1707.02942 [hep-th]
asymptotic safety guaranteed
Phys.Rev. D97 (2018) no.8, 085008
safety guaranteed in supersymmetry
Phys.Rev.Lett. 119 (2017) no.21, 211601
In search of a UV completion of the Standard
Model - 378.000 models that don't work
Andrew Bond, Daniel Litim, Gustavo Medina Vazquez and Tom Steudtner (2017)
UV conformal window for asymptotic safety
D97 (2018) no.3, 036019
safety of scalar field theories
of asymptotic safety
Gudrun Hiller, Clara Hormigos-Feliu, Daniel F. Litim, Tom Steudtner (2019)
Asymptotically safe extensions of the Standard Model with flavour phenomenologyarXiv:1905.11020 [hep-th]
Borut Bajc, Adrian Lugo and Francesco Sannino (2019)
Safe hologramarXiv:1910.07354 [hep-th]
Andrew Bond, Daniel F. Litim, Tom Steudtner (2019)
symptotic safety with Majorana fermions and new large N equivalencesarXiv:1911.11168 [hep-th]
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)
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).
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.
Guilherme de Berredo--Peixoto and Ilya L. Shapiro (2005)
Higher derivative quantum gravity with Gauss - Bonnet term.
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
Phys. Lett. B 632 (2006) 433
B. Holdom and J. Ren (2015)
QCD analogy for quantum
Phys. Rev. D93 (2016) 124030
John F. Donoghue (2016a)
Is the spin connection confined or condensed?
John F. Donoghue (2016b)
A conformal model of gravitons
John F. Donoghue (2017)
Quartic propagators, negative norms and the physical spectrum
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)
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
John F. Donoghue (1994a)
Leading quantum correction to the Newtonian potential.
John F. Donoghue (1994b)
General Relativity as an effective field theory:
The leading quantum corrections.
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.arXiv:gr-qc/9611018
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
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
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
John F. Donoghue (2016a)
Is the spin connection confined or condensed?arXiv:1609.03523 [hep-th]
John F. Donoghue (2016b)
A conformal model of
John F. Donoghue, Mikhail.M. Ivanov and Andrey Shkerin (2017a)
EPFL Lectures on General
Relativity as a Quantum Field Theory
John F. Donoghue (2017b)
Quartic propagators, negative
norms and the physical spectrum
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.
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
J. Ambjørn, A. Goerlich, J. Jurkiewicz, R. Loll (2008)
The Nonperturbative Quantum de Sitter Universe.
Phys. Rev. D78, 063544
J. Ambjørn, A. Goerlich, J. Jurkiewicz, R. Loll (2010)
CDT-an entropic theory of quantum gravity.
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)
Evidence for asymptotic safety from lattice quantum gravity.
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
A validation of Causal Dynamical Triangulations.
An independent numerical verification of the
results by the group of Ambjørn, Jurkiewicz and Loll.
Continuum limit in matrix models for quantum gravity from the functional renormalization group.
Flowing to the continuum in
discrete tensor models for quantum gravity
Towards coarse graining of
discrete Lorentzian quantum gravity
Class.Quant.Grav. 35 (2018) no.4, 044001
background-independent coarse-graining in tensor models
for quantum gravity
Spectral Methods and Running
Scales in Causal Dynamical Triangulations
Quantum spacetime and the
renormalization group: Progress and visions
L. Griguolo and R. Percacci (1995)
“The beta functions of a scalar theory coupled to gravity”,
Phys. Rev. D 52, 5787 (1995).
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
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).
Also finds a vanishing gravitational correction to the Yang-Mills beta function.
Yong Tang, Yue-Liang Wu (2008)
Gravitational Contributions to the Running of
Commun. Theor. Phys. 54, 1040 (2010)
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
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
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)
O. Zanusso, L. Zambelli, G.P. Vacca and R. Percacci (2009)
Gravitational corrections to Yukawa systems.
Phys. Lett. B689 90-94 (2010)
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
Phys. Rev. Lett. 104, 081301 (2010)
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
JHEP 1001, 084 (2010)
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
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.
O. Zanusso, G.P. Vacca
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.
Asymptotic safety in Einstein gravity and scalar-fermion matter.
Phys. Rev. Lett. 105, 231601 (2010)
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)
Mohamed M. Anber, John F.
Donoghue and Mohamed El-Houssieny (2010)
Running couplings and
operator mixing in the gravitational corrections to
Phys. Rev. D83, 124003 (2011)
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.
On the interpretation of gravitational corrections to gauge couplings.
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.
Asymptotic freedom of
Yang-Mills theory with gravity.
Phys. Lett. B709, 234-241 (2012)
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
QED coupled to QEG
JHEP 1105, 119 (2011)
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)
contributions to the beta function of quantum
Phys. Lett. B700, 86-89 (2011)
evaluation of the quadratic divergences due to gravity,
emphasizing the source of ambiguities.
Andreas Rodigast and Theodor Schuster (2011)
Gravitational corrections to non gauge
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.
On the running of the gravitational constant
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.
Hao-Ran Chang, Wen-Tao Hou and Yi Sun (2012)
Gravitational corrections to phi^4 theory with spontaneously broken symmetry
Artur R. Pietrykowski (2012)
Interacting scalar fields in the context of effective quantum gravity
G. Narain and R. Anishetty (2012)
Charge renormalization due to graviton loops
JHEP 1307 (2013)
G. Narain and R. Anishetty (2013)
Running couplings in quantum theory of gravity
coupled to gauge fields
JHEP 1310 (2013)
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?
calculate the gravitational correction to the beta
functions of scalar and Yukawa couplings both in GR and in