Applications of asymptotically safe gravity

Other nonperturbatively renormalizable theories and applications

Classic papers on quantum gravity

Euclidean quantum gravity

Effective field theory of gravity

Discrete gravity

Gravitational effects on matter couplings

Other relevant papers

Papers on asymptotic safety of gravity.

**Steven
Weinberg (1976)**

Critical
Phenomena for Field Theorists.

Lectures
presented at Int. School of Subnuclear Physics, Ettore
Majorana, Erice, Sicily, Jul 23 -
Aug 8, 1976.

Published in Erice Subnucl. Phys.1976:1

**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.

**Steven
Weinberg (1979)**

Ultraviolet
divergences in quantum theories of gravitation.

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

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

**Lee
Smolin (1982)**

A
fixed point for quantum gravity.

Nucl.
Phys. B 208, 439-466

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

**Hikaru
Kawai and Masao Ninomiya (1990)**

Renormalization
group and quantum gravity.

Nuclear
Physics B 336, 115-145

*This
paper discusses several issues related to the application of
the renormalization group to quantum gravity, in particular
in relation to the ε expansion. It is
observed that due to its nontrivial dimensionality, the
running of *

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

The
Epsilon expansion of two-dimensional quantum gravity.

Nucl.Phys.B358,
695-712

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

Scaling
exponents in quantum gravity near two-dimensions.

Nucl.
Phys. B393, 280-300

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

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

Nucl.
Phys. B404, 684-716

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

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

Nucl.
Phys. B427, 158-180

**Jun
Nishimura, Shinya Tamura, Asato Tsuchiya (1994)**

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

Mod.
Phys. Lett. A9, 3565-3574

**Hikaru
Kawai, Yoshihisa Kitazawa, Masao Ninomiya (1996)**

Renormalizability
of quantum gravity near two-dimensions.

Nucl.
Phys. B467, 313-331

**T.
Aida and Y. Kitazawa (1997)**

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

Nucl.
Phys. B 491, 427.

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

**Martin
Reuter (1996)**

Nonperturbative
evolution equation for quantum gravity.

Phys.
Rev. D57, 971.

*In
this paper the ERGE is written for gravity. It is then
truncated and the beta functions for *

**Djamel
Dou and Roberto Percacci (1998)**

The
running gravitational couplings.

Class.
Quant. Grav. 15, 3449

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

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

Exact
renormalization group for O(4)
gauged supergravity.

Phys.
Lett. B409 206-212

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

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

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

JETP
Lett. 65, 600-604

*Here,
using the ERGE, the effect of an R ^{2} term on the
running of *

**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 R ^{2} is computed starting
from the Einstein-Hilbert truncation of the action. The
contribution of the coupling η to its own beta function is
not taken into account.*

**Sven
Falkenberg, Sergei D. Odintsov (1998)**

Gauge
dependence of the effective average action in Einstein
gravity.

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

*Talk
given at the 8th Marcel Grossmann Meeting.*

**Wataru
Souma (1999)**

Nontrivial
ultraviolet fixed point in quantum gravity.

Prog.
Theor. Phys. 102, 181.

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

**Wataru
Souma (2000)**

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

**Martin
Reuter (2000)**

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.

*The
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.

*Here
the ERGE is applied to a truncation involving* *a
term η R^{2} (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.

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

**Roberto
Percacci and Daniele Perini (2004)**

On
the ultraviolet behaviour of Newton's constant.

Class.
and Quantum Grav. 21, 5035.

*This
paper discusses an apparent puzzle in asymptotically safe
gravity.* *It is noted that *

**Alfio
Bonanno, Martin Reuter (2005)**

Proper
time flow equation for gravity.

JHEP
0502, 035

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

**Oliver
Lauscher and Martin Reuter (2005)**

Fractal
spacetime structure in asymptotically safe gravity.

JHEP
0510, 050

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

**Martin
Reuter and Jan-Markus Schwindt (2006)**

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

JHEP
0601, 070

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

**Oliver
Lauscher, Martin Reuter (2005)**

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

In
“Quantum gravity” , ed. B. Fauser, J. Tolksdorf and

*Invited
talk at 14th Oporto Meeting
on Geometry, Topology and Physics: Mathematical Aspects of
Quantum Field Theory, Oporto, *

**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

http://relativity.livingreviews.org/Articles/lrr-2006-5/

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

**Peter
Fischer, Daniel F. Litim (2006)**

Fixed
points of quantum gravity in extra dimensions.

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

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

**Daniel
F. Litim (2006)**

On
fixed points of quantum gravity.

AIP
Conf. Proc. 841, 322-329 (2006).

Also in *Oviedo

*Talk
presented at 28th Spanish Relativity Meeting (ERE05): A
Century of Relativity Physics, Oviedo,
Asturias,
*

**Peter
Fischer, Daniel F. Litim (2006)**

Fixed
points of quantum gravity in higher dimensions.

AIP
Conf. Proc. 861, 336-343 (2006).

Also in *Paris 2005, Albert Einstein's century* 336-343

*Talk
presented at Albert Einstein's Century International
Conference, *

**Max
Niedermaier (2007)**

The
Asymptotic safety scenario in quantum gravity: An
Introduction.

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

**Roberto
Percacci (2007a)**

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

J.
Phys. A40, 4895-4914

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

**Alessandro
Codello, Roberto Percacci (2006)**

Fixed
points of higher derivative gravity.

Phys.
Rev. Lett. 97, 221301

*This
paper establishes a link between old literature on higher
derivative* *gravity (references given below) and the
approach to asymptotic safety based on the ERGE. It contains
a one loop recalculation of the beta functions of a theory
containing arbitrary
terms with up to four derivatives of the metric. The old
results are reproduced for the dimensionless couplings,*
*but in the case of *

**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)**

Asymptotic
Safety.

*In
'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

arXiv:0712.0445 [hep-th]

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

**Martin
Reuter and Holger Weyer (2008a)**

Background
independence and asymptotic safety in conformally reduced
gravity

Phys. Rev. D79, 105005 (2009)

*This
paper discusses the RG flow in conformally reduced gravity,
meaning that only the conformal degree of freedom is
retained. There is a detailed discussion of the proper way
of defining the cutoff in such a theory, where the role of
“background independence” is emphasized. It is shown that,
perhaps surprisingly, this reduced dynamics by itself has a
fixed point for *

**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 R ^{2} and Weyl^{2} 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

arXiv:0904.2510 [hep-th]

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

**Elisa
Manrique and Martin Reuter (2009a)**

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

**PoS CLAQG08 (2011)
001**

arXiv:0905.4220
[hep-th]

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

**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)**

Effective
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)**

Acta phys, Polon. B40 3439-3457 (2009)

arXiv:0910.5390 [hep-th]

**Gaurav
Narain and Roberto Percacci (2009b)**

Class. and Quantum Grav. 27, 075001 (2010)

arXiv:0911.0386 [hep-th]

**Gaurav
Narain and Christoph Rahmede (2009)**

Class. and Quantum Grav. 27, 075002 (2010)

arXiv:0911.0394 [hep-th]

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

**Max
Niedermaier (2009)**

Gravitational
fixed points from perturbation theory.

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

**Kai
Groh and Frank Saueressig(2010)**

Ghost
wave function renormalization in asymptotically safe quantum
gravity.

J.
Phys. A43 365403 (2010).

*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)**

Matter
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)**

Bimetric
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)**

Asymptotic
safety, emergence and minimal length

Class. and Quantum Grav. 27, 245026

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

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

The
universal RG machine

JHEP 1106, 079 (2011)

**Jan-Erik
Daum and Martin Reuter (2010a)**

Renormalization
group flow of the Holst action

Phys.Lett. B710 (2012) 215-218

**Jan-Erik
Daum and Martin Reuter (2011)**

Running
Immirzi parameter and asymptotic safety

PoS CNCFG2010, 003 (2010)

arXiv:1111.0991
[hep-th]

**Alessandro Codello and Omar Zanusso (2011)**

Fluid membranes and 2d quantum gravity

Phys. Rev. D83 125021 (2011)

The authors compute the beta functions of a theory of two dimensional surfaces embedded in a D-dimensional Euclidean space. The action contains three terms, corresponding to surface tension, intrinsic curvature and extrinsic curvature. The limit D->0, corresponding to two dimensional gravity, is then studied.

**Elisa
Manrique, Stefan Rechenberger and Frank Saueressig (2010)**

Asymptotically
safe Lorentzian gravity

Phys. Rev. Lett. 106 251302 (2011)

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

**Gian
Paolo Vacca and Luca Zambelli (2011)**

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

Phys. Rev. D83 125024 (2011)

Dario Benedetti and Simone Speziale (2011)

Perturbative
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)**

Light
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)**

Asymptotic
safety goes on shell

New J. of Phys. 14, 015005 (2012)

**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)

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

**Astrid
Eichhorn (2011)**

Observable
consequences of quantum gravity: can light fermions exist?

J. Phys. Conf. Ser. 360, 012057 (2012)

Martin Reuter and Frank Saueressig (2011)

Fractal
space-times under the microscope: a renormalization group
view of Monte Carlo data

JHEP 1112, 012 (2011)

**Roberto
Percacci (2011a)**

A short introduction to asymptotic safety.

**Roberto
Percacci (2011b)**

RG
flow of Weyl-invariant dilaton gravity.

New J. of Phys. 13, 125013 (2011)

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

Higher
derivative gravity from the universal renormalization group
machine

PoS EPS-HEP 2011 124 (2011)

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

** ****Kai
Groh, ****Frank Saueressig ****and
Omar Zanusso (2011)**

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

**
Martin Reuter and Frank Saueressig ****(2012a)**

Quantum
Einstein Gravity

The "tetrad only" theory space: nonperturbative
renormalization flow and asymptotic safety

JHEP 1205 (2012) 005

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

The phase diagram of quantum gravity from
diffeomorphism invariant RG flows

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

**Astrid
Eichhorn (2012)**

Quantum
gravity-induced matter self-interactions in the asymptotic
safety scenario

Phys. Rev. D86, 105021 (2012)

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

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

Infrared
fixed point in quantum Einstein gravity

JHEP 1207 (2012) 102

**Dario
Benedetti and Francesco Caravelli (2012)**

The
local potential approximation in quantum gravity

JHEP 1206 (2012) 017, Erratum-ibid. 1210 (2012) 157

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

**Nobuyoshi
Ohta (2012)**

Beta
function and asymptotic safety in three dimensional higher
derivative gravity

**Class.Quant.Grav. 29 (2012) 205012**

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

Running boundary actions, asymptotic safety and
black hole thermodynamics

JHEP 1207 (2012) 172

Limit cycles and quantum gravity

**
Martin Reuter and Frank Saueressig ****(2012b)**

Asymptotic
safety, fractals and cosmology

**
Stefan Rechenberger and Frank Saueressig ****(2012)**

The
R^2 phase diagram of QEG and its spectral dimension

Phys.Rev. D86 (2012) 024018

arXiv:1206.0657
[hep-th]

**Alfio
Bonanno and Filippo Guarnieri (2012)**

Universality and symmetry breaking in conformally reduced quantum gravity

Phys.
Rev. D 86, 105027 (2012)

arXiv:1206.6531 [hep-th]

**
Andreas Nink and Martin Reuter ****(2012)**

On
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)**

Fixed-functionals
of three-dimensional Quantum Einstein Gravity

JHEP 1211 (2012) 131

arXiv:1208.2038
[hep-th]

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

Fixed
points and infrared completion of quantum gravity

**Phys.Lett. B728 (2014) 114-117**

**Roberto
Percacci and Pietro Dona' (2012)**

Functional
renormalization with fermions and tetrads

Phys.Rev. D87 (2013) 045002

arXiv:1209.3649
[hep-th]* *

The gravitational beta functions had been worked out in tetrad formalism by Harst and Reuter (2012). Here the analysis is extended by considering more general cutoff types (type I or II, with or without using the York decomposition), and with a gauge parameter. It appears that when the York decomposition is used the results are much less sensitive to mu, and resemble those of the metric formalism even for mu tending to infinity (which corresponds to dropping the Lorentz ghost contribution). Pathologies reappear when the gauge parameter becomes of order two.

**Astrid
Eichhorn (2012)**

Experimentally testing asymptotically safe quantum gravity with photon-photon scattering

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

Renormalization
group and Weyl invariance.

Class.Quant.Grav. 30 (2013) 115015

**S.
Nagy (2012)**

Lectures
on renormalization and asymptotic safety

Ann. Phys. (2013) 310-346

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

Asymptotic
safety in the f(R) approximation

JHEP 1301 (2013) 108

arXiv:1211.0955
[hep-th]

Asymptotic safety and black hole thermodynamics

**
Andreas Nink and Martin Reuter ****(2012)**

On
quantum gravity, asymptotic safety and paramagnetic dominance

Astrid Eichhorn (2013b)

On
unimodular quantum gravity

Class.Quant.Grav. 30 (2013) 115016

**Astrid
Eichhorn (2013a)**

Faddeev-Popov
ghosts in quantum gravity beyond perturbation theory

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

**
Stefan Rechenberger and Frank Saueressig ****(2012)**

A
functional renormalization group equation for foliated
spacetimes

**JHEP 1303 (2013) 010**

**Dario
Benedetti (2013)**

On the number of relevant operators in asymptotically safe gravity

**Europhys.Lett. 102 (2013) 20007**

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

A
bootstrap towards asymptotic safety

**Jan-Eric
Daum, Martin Reuter (2013)**

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

**Annals Phys. 334 (2013) 351-419**

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

Beta
functions of topologically massive supergravity

**JHEP 1403 (2014) 083**

**Alfio
Bonanno, Martin Reuter (2013)**

Modulated
ground state of gravity theories with stabilized conformal
factor.

Phys. Rev. D.87, 084019

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

Consistent
closure of RG flow equations in quantum gravity

**Phys.Rev. D89 (2014) 081701**

Probing the quantum nature of
spacetime by diffusion

Phys.Rev. D87 (2013) 12, 124028

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

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

JHEP 1307 (2013) 064

**Nobuyoshi
Ohta and Roberto Percacci (2013)**

Higher
derivative gravity and asymptotic safety in diverse
dimensions

**Class.Quant.Grav. 31 (2014) 015024**

**Dario
Benedetti and Filippo Guarnieri (2013)**

Brans-Dicke
theory in the local potential approximation

**New J.Phys. 16 (2014) 053051**

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

Matter
matters in asymptotically safe quantum gravity

Phys.Rev. D89 (2014) 084035

**Carlo
Pagani and Roberto Percacci (2013)**

Quantization
and fixed points of non-integrable Weyl theory

Class. Quant. Grav. 31 (2014) 115005

**
Maximilian Demmel****, Stefan Rechenberger and Omar Zanusso (2014)**

RG
flows of Quantum Einstein Gravity on maximally symmetric
spaces

JHEP 1406 (2014) 026

arXiv:1401.5495
[hep-th]

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

**
Nicolai Christiansen, Jan Pawlowski and Andreas Rodigast ****(2014)**

Global
flows in quantum gravity

Phys.Rev. D93 (2016) no.4, 044036

En route to background independence: broken
split-symmetry and how to restore it with bi-metric
average actions.

Annals Phys. 350 (2014) 225-301

Propagating gravitons vs. dark matter in
asymptotically safe quantum gravity

JHEP 1412 (2014) 025

Using the results of the double-Einstein-Hilbert truncations studied in Manrique, Reuter, Saueressig (2010b) and Becker and Reuter (2014a) it is shown that when the

Kevin Falls (2014)

Asymptotic
safety and the cosmological constant

JHEP 1601 (2016) 069

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

Consistency
of matter models with asymptotically safe quanum gravity

Canadian Journal of Physics, 2015, 93(9): 988-994

*Proceedings
of Theory Canada 9.*

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

Further
evidence for asymptotic safety of quantum gravity

Phys.Rev. D93 (2016) no.10, 104022

**Ippocratis
Saltas (2014)****
**

On the UV structure of quantum unimodular gravity

Andreas Nink

Field
parametrization dependence in asymptotically safe quantum
gravity

Phys.Rev. D91 (2015) 4, 044030

A new functional flow equation for
Einstein-Cartan quantum gravity

Annals Phys. 354 (2015) 637-704

arXiv:1410.7993
[hep-th]

In order to ease the technical difficulties encountered in the application of the ERGE to Einstein-Cartan theory (Daum and Reuter) this paper develops and then uses a "special purpose" simplified functional equation

Towards a C-function in quantum gravity

JHEP 1503 (2015) 065

**Alessandro
Codello, Giulio d'Odorico (2014)**

Scaling
and renormalization in two-dimensional quantum gravity

Phys.Rev. D92 (2015) 2, 024026

**
Maximilian Demmel, Frank Saueressig ****and
Omar Zanusso (2014)**

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

Annals
Phys. 359 (2015) 141-165

arXiv:1412.7207
[hep-th]

**Roberto
Percacci and Gian Paolo Vacca (2015a)**

Search
of scaling solutions in scalar-tensor gravity

Eur.Phys.J. C75 (2015) 5, 188

arXiv:1501.00888
[hep-th]* *

**Kevin
Falls (2015)**

On
the renormalization of Newton's constant

Phys.Rev. D92 (2015) no.12, 124057

**Astrid
Eichhorn (2015)**

The
renormalization group flow of unimodular f(R) gravity

JHEP 1504 (2015) 096

**Julia
Borchardt and Benjamin Knorr (2015)**

Global
solutions of functional fixed point equations via
pseudo-spectral methods

Phys.Rev. D91 (2015) 10, 105011

arXiv:1502.07511
[hep-th]* *

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

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

Background-independent
exact renormalization group for conformally reduced gravity

JHEP 1504 (2015) 118

**
Maximilian Demmel, Frank Saueressig ****and
Omar Zanusso (2015)**

A
proper fixed functional for four-dimensional Quantum Einstein
Gravity

JHEP 1508 (2015) 113

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

Asymptotic
safety in O(N) scalar models coupled to gravity

Phys.Lett. B753 (2016) 274-281

arXiv:1505.05393
[hep-th]* *

Connections
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)**

Local
quantum gravity

Phys.Rev. D92 (2015) no.12, 121501

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

Flow
equation for f(R) gravity and some of its exact solutions

Phys. Rev. D92 (2015) 6, 061501

arXiv:1507.00968
[hep-th]* *

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

JHEP 1511 (2015) 094

arXiv:1507.08657 [hep-th]

**Holger
Gies, Benjamin Knorr and Stefan Lippoldt (2015)**

Generalized
Parametrization Dependence in Quantum Gravity

Phys.Rev. D92 (2015) no.8, 084020

The metric on field space, functional
renormalization and metric-torsion quantum gravity

Ann. Phys. (2016)

**
Kin-ya Oda and Masatoshi Yamada ****(2016)**

Non-minimal
coupling in Higgs–Yukawa model with asymptotically safe
gravity

Class.Quant.Grav. 33 (2016) no.12, 125011

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

Asymptotic
safety of gravity-matter systems

Phys.Rev. D93 (2016) no.8,
084035

On selfdual spin-connections and Asymptotic
Safety

Phys.Lett. B753 (2016) 395-400

**Dario
Benedetti (2015)**

Gen.Rel.Grav. 48 (2016) no.5, 68

arXiv:1511.06560 [hep-th]

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

Renormalization
Group Equation and scaling solutions for f(R) gravity in
exponential parametrization

European Physical Journal C (2016) 76:46

arXiv:1511.09393
[hep-th]* *

The unitary conformal field theory behind 2D
asymptotic safety

JHEP 1602 (2016) 167

arXiv:1512.06805[hep-th]

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

Asymptotic
safety in an interacting system of gravity and scalar matter

Phys.Rev. D93 (2016) no.4, 044049

Asymptotically
safe R+R^2 Gravity

PoS CORFU2016

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

Phys.Rev.Lett. 116 (2016) no.21, 211302

**
Jan Meibohm, Jan Pawlowski ****(2016)**

Chiral
fermions in asymptotically safe quantum gravity

Eur.Phys.J. C76 (2016) no.5, 285

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

JHEP 1606 (2016) 012

arXiv:1602.08993 [hep-th]

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

Phys.Rev. D94 (2016) no.2, 024007

arXiv:1603.04772 [hep-th]

**
Astrid Eichhorn, Aaron Held and Jan Pawlowski ****(2016)**

Quantum
gravity effects on a Higgs-Yukawa model

Phys.Rev. D94 (2016) no.10, 104027

arXiv:1604.02041
[hep-th]

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

Gauges
and functional measures in quantum gravity I: Einstein
theory

JHEP 1606 (2016) 115

arXiv:1505.00454
[hep-th]* *

**
Tobias Henz, Jan Pawlowski and Christoph Wetterich ****(2016)**

Scaling
solutions for Dilaton Quantum Gravity

Phys.Lett. B769 (2017) 105-110

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

Phys.Rev. D94 (2016) no.12, 124014

arXiv:1605.07636 [hep-th]

**Nobuyoshi
Ohta and Kevin Falls (2016)**

Renormalization
Group Equation for f(R) gravity on hyperbolic spaces

Phys.Rev. D94 (2016) no.8, 084005

arXiv:1507.08460
[hep-th]* *

Quantum
gravity on foliated spacetime - asymptotically safe and
sound

Phys.Rev. D95 (2017) no.8, 086013

**
Tim R. Morris ****(2016)**

JHEP 1611 (2016) 160

arXiv:1610.03081 [hep-th]

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

Gauges
and functional measures in quantum gravity II: higher
derivative gravity

Eur.Phys.J. C77 (2017) no.9, 611

arXiv:1610.07991
[hep-th]* *

**
Astrid Eichhorn and Stefan Lippoldt ****(2016)**

Phys.Lett. B767 (2017) 142-146

arXiv:1611.05878 [hep-th]

**
Carlo Pagani and Martin Reuter ****(2016)**

Phys.Rev. D95 (2017) no.6, 066002

arXiv:1611.06522 [hep-th]

**Roberto
Percacci and Gian Paolo Vacca (2016)**

The background scale Ward identity in quantum gravity

Eur.Phys.J. C77 (2017) no.1, 52

arXiv:1611.07005
[hep-th]* *

**
Nicolai Christiansen ****(2016)**

Four-derivative
quantum gravity beyond perturbation theory

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

Towards
apparent convergence in asymptotically safe quantum gravity

Eur.Phys.J. C78 (2018) no.4, 336

Background
scale independence in quantum gravity

PTEP 2017 (2017) no.3, 033E02

arXiv:1701.01506
[hep-th]

**Kevin
Falls (2017)**

Physical
renormalization schemes and asymptotic safety in quantum
gravity

Phys.Rev. D96 (2017) no.12, 126016

arXiv:1702.03577
[hep-th]

Renormalization
group fixed points of foliated gravity-matter systems

JHEP 1705 (2017) 093

**
Astrid Eichhorn and Nicolai Christiansen ****(2017)**

An
asymptotically safe solution to the U(1) triviality problem

Phys.Lett. B770 (2017) 154-160

**Yuta
Hamada and Masatoshi Yamada ****(2017)**

arXiv:1703.09033 [hep-th]

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

Phys.Rev. D95 (2017) no.10, 106010

arXiv:1704.08873 [hep-th]

Impact
of topology in foliated Quantum EInstein Gravity

Is
scale-invariance in gauge-Yukawa systems compatible with the
graviton?

Phys.Rev. D96 (2017) no.8, 084021

Top
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)**

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

Split Weyl transformations in quantum gravity

Phys.Rev. D96 (2017) no.10, 106019

arXiv:1708.09760 [hep-th]

**
Astrid Eichhorn ****(2017)**

Found.Phys. 48 (2018) no.10, 1407-1429

arXiv:1709.03696 [hep-th]

Upper
bound on the abelian gauge coupling from asymptotic safety

JHEP 1801 (2018) 030

On
avoiding Ostrogradski instabilities within asymptotic safety

JHEP 1712 (2017) 121

Functional
renormalization group flows on
Friedmann-Lemaitre-Robertson-Walker backgrounds

Found.Phys. 48 (2018) no.10, 1291-1304

**
Astrid Eichhorn, Stefan Lippoldt and Vedran Skrinjar ****(2017)**

Phys.Rev. D97 (2018) no.2, 026002

arXiv:1710.03005 [hep-th]

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

Asymptotic
safety of gravity with matter

(Formerly" One force to rule them all: asymptotic safety of
gravity with matter")

Phys.Rev. D97 (2018) no.10, 106012

**
Benjamin Knorr ****(2017)**

Infinite
order quantum-gravitational correlations

Class.Quant.Grav. 35 (2018) no.11, 115005

**
Astrid Eichhorn, Aaron Held and Christof Wetterich ****(2017)**

Phys.Lett. B782 (2018) 198-201

arXiv:1711.02949 [hep-th]

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

Curvature
dependence of quantum gravity

Phys.Rev. D97 (2018) no.4, 046007

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

Phys.Rev. D97 (2018) no.8, 086004

arXiv:1712.00319 [hep-th]

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

The Effects of Running
Gravitational Coupling On Rotating Black Holes

Eur.Phys.J. C78 (2018) 519

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

Asymptotic
safety of quantum gravity beyond Ricci scalars

Phys.Rev. D97 (2018) no.8, 086006

**
Tim R. Morris ****(2018)**

JHEP 1808 (2018) 024

arXiv:1802.04281 [hep-th]

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

JHEP 1808 (2018) 147

arXiv:1802.08589 [hep-th]

**Natalia
Alkofer and Frank Saueressig ****(2018)**

Annals Phys. 396 (2018) 173-201

arXiv:1802.00498 [hep-th]

Cosmological
bounds on the field content of asymptotically safe
gravity–matter models

Phys.Lett. B784 (2018) 229-236

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

Phys.Rev. D94 (2016) no.2, 024007

arXiv:1804.00012 [hep-th]

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

Class.Quant.Grav. 35 (2018) no.17, 175002

arXiv:1803.00859 [hep-th]

**
Carlo Pagani and Martin Reuter ****(2018)**

JHEP 1807 (2018) 039

arXiv:1804.02162 [hep-th]

Towards
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)**

Asymptotic
safety and field parametrization dependence in the f(R)
truncation

Phys.Rev. D98 (2018) no.2, 026027

arXiv:1805.09656
[hep-th]

* *

**Gabriele Gionti
(2018)**

Hamiltonian
Analysis of Asymptotically Safe Gravity

**Natalia
Alkofer ****(2018)**

arXiv:1809.06162 [hep-th]

Simon Friederich **(2018)**

Stud.Hist.Philos.Mod.Phys. 63 (2018) 65-73

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

Aspects
of asymptotic safety for quantum gravity

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

Phys.Lett. B792 (2019) 310-314

arXiv:1810.02828 [hep-th]

**
Astrid Eichhorn ****(2018)**

Front.Astron.Space Sci. 5 (2019) 47

arXiv:1810.07615 [hep-th]

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

Phys.Rev. D99 (2019) no.8, 086010

arXiv:1811.11706 [hep-th]

d=4 as the critical dimensionality of asymptotically safe interactions

arXiv:1902.06479 [hep-th]

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

arXiv:1905.11114 [hep-th]

**
Christof Wetterich ****(2019)**

arXiv:1901.04741 [hep-th]

**
Christof Wetterich, Masatoshi Yamada ****(2019)**

arXiv:1906.01721 [hep-th]

**Carlo
Pagani, Martin Reuter (2019)**

Background
Independent Quantum Field Theory and Gravitating Vacuum
Fluctuations

Phys.
Rev. D60, 084011

Form
factors in asymptotic safety: conceptual ideas and
computational toolbox

Class.Quant.Grav. 36 (2019) no.23, 234001

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

Phys.Lett. B798 (2019) 134991

arXiv:1907.07974 [hep-th]

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

JHEP 1909 (2019) 100

arXiv:1907.11173 [hep-th]

Predictive power of grand unification from quantum gravity

arXiv:1909.17318 [hep-th]

**John
Donoghue (2019)**

A
critique of the asymptotic safety program

**Applications
of
asymptotically
safe gravity**

**Alfio
Bonanno, Martin Reuter (1999)**

Quantum
gravity effects near the null black hole singularity.

Phys.
Rev. D60, 084011

**Alfio
Bonanno, Martin Reuter (2000)**

Renormalization
group improved black hole spacetimes.

Phys.
Rev. D 62, 043008.

*This
paper discusses the geometry of a black hole taking into
account the RG flow of *

**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)**

Running

Phys.Rev.D70,
124028

**Martin
Reuter and Frank Saueressig (2005)**

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

JCAP
09, 012.

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

**B.F.L.
Ward (2006)**

Planck
Scale Remnants in Resummed Quantum Gravity

Acta
Phys. Polon. B37, 1967-1974

arXiv: hep-ph/0605054

**Hiroki
Emoto (2005)**

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

**Hiroki
Emoto (2006)**

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

**Alfio Bonanno,
Martin Reuter (2006)**

Spacetime
structure of an evaporating black hole in quantum gravity.

Phys.
Rev. D73, 083005

**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

*The
scale dependence of *

**Daniel
F. Litim and Tilman Plehn (2008)**

Signatures
of gravitational fixed points at the LHC.

Phys.
Rev. Lett. 100, 131301

*Takes
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

arXiv:808.3124 [gr-qc]

**Alfio Bonanno,
Martin Reuter (2008)**

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

J.
Phys. Conf. Ser.140, 012008

**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

arXiv:0910.0490[gr-qc]

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)

arXiv:0912.0208 [hep-th]

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

**Martin
Reuter and E. Tuiran (2009)**

Quantum
Gravity Effects in the Kerr spacetime

Phys. Rev. D83, 044041 (2011)

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

Black
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)**

Asymptotic
Safety, Asymptotic Darkness, and the hoop conjecture in the
extreme UV.

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)**

Black
holes in an asymptotically safe gravity theory with higher
derivatives.

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)**

Inflationary
solutions in
asymptotically safe f(R) gravity

Class. and Quantum Grav. 28, 145026 (2011)

*This
paper d**iscusses 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)**

Asymptotic
safety, singularities and gravitational collapse

Phys. Lett. B695, 317-319 (2011)

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

Deformed
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)

Comments
on asymptotically safe inflation

Phys. Rev. D82, 127302 (2010)

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

Planck
scale cosmology and asymptotic safety in Resummed Quantum
Gravity

PoS ICHEP 2010:477 (2010)

Asymptotic
safety and Kaluza-Klein gravitons at the LHC.

Phys. Rev. D83 084048 (2011)

**Mark
Hindmarsh, Daniel Litim and Christoph Rahmede (2011)**

Asymptotically
safe cosmology

JCAP 1107, 019 (2011)

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

From
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)

Asymptotically
safe gravity as a scalar-tensor theory and its cosmological
implications

Phys. Rev. D84, 103502 (2011)

**Adriano
Contillo, Mark Hindmarsh and Christoph Rahmede (2011)**

Renormalization
group improvement of scalar field inflation

Phys. Rev. D85, 043501 (2012)

The
Possibility of Inflation in Asymptotically Safe Gravity

**Alfio Bonanno
(2012)**

An
effective action for asymptotically safe gravity

Phys.Rev. D85 (2012) 081503

**Mark
Hindmarsh and Ippocrates Saltas (2012)**

f(R)
gravity from the renormalisation group

Phys.Rev. D86 (2012) 064029

**Babette
Dobrich and Astrid Eichhorn (2012)**

Can
we see quantum gravity? Photons in the asymptotic-safety
scenario.

JHEP 206, 156 (2012)

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

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

Higgs
boson mass and new physics

JHEP 1210 (2012) 140

**Christopher
Estrada and Matilde Marcolli (2012)**

Asymptotic
safety, hypergeometric functions and the Higgs mass in
spectral action models

Int.J.Geom.Meth.Mod.Phys. 10 (2013) 1350036

arXiv:1208.5023
[hep-th]

Anja Marunovic and Tomislav Prokopec (2012)

On
antiscreening in perturbative quantum gravity and resolving
the Newtonian singularity

The
trouble with asymptotically safe inflation.

**Kevin
Falls and Daniel F. Litim (2012)**

Black
hole thermodynamics under the microscope

Phys.Rev. D89 (2014) 084002

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

Planck
constraints on Higgs modulated reheating of renormalization
group improved inflation

Phys.Rev. D88 (2013) 083508

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

Dilaton quantum gravity

**Edmund
Copeland, Christoph Rahmede and Ippocratis Saltas (2013)**

Asymptotically
safe Starobinski inflation

Structural
aspects of asymptotically safe black holes.

Class. and Quantum Grav. 31 (2013) 015006

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

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

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

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

Black
holes and running couplings: a comparison of two
complementary approaches

Springer Proc.Phys. 170 (2016) 263-269

Inflation, quintessence and the origin of mass

Nucl.Phys. B897 (2015) 111-178

Scale
Setting for Self-consistent Backgrounds

Phys.Rev. D91 (2015) no.2, 025009

Black
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)

Avoidance
of singularities in asymptotically safe Quantum Einstein
Gravity

JCAP 1510 (2015) no.10, 069

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

Asymptotically
safe Higgs inflation

Asymptotically
safe inflation from quadratic gravity

Phys.Lett. B750 (2015) 638-642

**Georgios
Kofinas, Vasilios Zarikas**** **(2015)

Asymptotically
Safe gravity and non-singular inflationary Big Bang with
vacuum birth

Phys.Rev. D94 (2016) no.10, 103514

Setting
the Renormalization Scale in QFT

J.Phys.Conf.Ser. 720 (2016) no.1, 012020

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

On
de Sitter solutions in asymptotically safe f(R) theories

Class.Quant.Grav. 35 (2018) no.13, 135006

Cosmic
Censorship in Quantum Einstein Gravity

Class.Quant.Grav. 34 (2017) no.9, 095012

**
Christof Wetterich and Masatoshi Yamada ****(2016)**

Gauge
hierarchy problem in asymptotically safe gravity - the
resurgence mechanism

Phys.Lett. B770 (2017) 268-271

**Alfio Bonanno
and Frank Saueressig (2017)**

Asymptotically
safe cosmology - a status report

Comptes Rendus Physique 18 254-264

Asymptotically
Safe gravitational collapse: Kuroda-Papapetrou RG-improved
model

PoS CORFU2016 (2017) 058

**R. Moti, A.
Shojai (2017)**

On
the effect of renormalization group improvement on the
cosmological power spectrum

Eur.Phys.J. C78 (2018) no.1, 32

**Ramon Torres
(2017)**

Nonsingular
black holes, the cosmological constant, and asymptotic safety

Phys.Rev. D95 (2017) no.12, 124004

**Georgios
Kofinas, Vasilios Zarikas**** **(2017)

A
solution of the dark energy and its coincidence problem
based on local antigravity sources without fine-tuning or
new scales

Phys. Rev. D 97, 123542 (2018)

**Alfio Bonanno,
Gabriele Gionti and Alessia Platania (2017)**

Bouncing
and emergent cosmologies from ADM RG flows

**
Astrid Eichhorn, Aaron Held ****(2018)**

Mass
difference for charged quarks from quantum gravity

Phys.Rev.Lett. 121 (2018) no.15, 151302

**
Astrid Eichhorn, Aaron Held and Christof Wetterich ****(2017)**

Quantum-gravity
predictions for the fine-structure constant

Phys.Lett. B782 (2018) 198-201

Singularity
from star collapse, torsion and asymptotic safety of gravity

**Yuexin Zhang,
Menglei Zhou and Cosimo Bambi (2018)**

Iron
line spectroscopy of black holes in asymptotically safe
gravity

Eur.Phys.J. C78 (2018) no.5, 376

Inflation
in an effective gravitational model & asymptotic safety

Phys.Rev. D98 (2018) no.4, 043505

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

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

Constraining
the Asymptotically Safe Cosmology: cosmic acceleration
without dark energy

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

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

JCAP 1812 (2018) no.12, 004

Asymptotic
safety, cosmology and Conformal Standard Model

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

**Jan M.
Pawlowski, Dennis Stock (2018)**

Quantum-improved
Schwarzschild-(A)dS and Kerr-(A)dS spacetimes

Phys.Rev. D98 (2018) no.10, 106008

**Vasilios
Zarikas**** and **** Georgios Kofinas **(2018)

Singularities
and Phenomenological aspects of Asymptotic Safe Gravity

J.Phys.Conf.Ser. 1051 (2018) no.1, 012028

**Ademola
Adeifoba, Astrid Eichhorn and Alessia Platania (2018)**

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

Asymptotic
safety and conformal standard model

**Astrid
Eichhorn, Stefan Lippoldt, Marc Schiffer (2018)**

Zooming in on fermions and quantum gravity

arXiv:1812.08782 [gr-qc]Scales
and hierachies in asymptotically safe quantum gravity: a
review

**Astrid
Eichhorn, Marc Schiffer (2019)**

d=4 as the critical dimensionality of asymptotically safe interactions

arXiv:1902.06479 [gr-qc]**Lando Bosma, Benjamin Knorr and Frank
Saueressig (2019)**

Resolving Spacetime Singularities within Quantum Gravity

**Aaron Held,
Roman Gold, Astrid Eichhorn (2019)**

Asymptotic safety casts its shadow

arXiv:1904.07133 [gr-qc]**Alessia Platania
(2019)**

The inflationary mechanism in Asymptotically Safe Gravity

arXiv:1908.03897 [gr-qc]

Giorgio Parisi (1975)

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

Nucl. Phys. B100 368

K. Gawedzki, A. Kupiainen (1985c)

Rigorous Renormalization Group - Asymptotic Freedom And Nongaussian Fixed Points.

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

K. Gawedzki, A. Kupiainen (1985b)

Renormalization Of A Nonrenormalizable Quantum Field Theory.

Nucl.Phys.B262 33

K. Gawedzki, A. Kupiainen (1985a)

Renormalizing The Nonrenormalizable.

Phys. Rev. Lett. 55 363-365

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

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

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

Phys. Rev. Lett. 66 3233-3236

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

D.I. Kazakov (2003).

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

JHEP 03, 020.

Holger Gies (2003)

Renormalizability of gauge theories in extra dimensions.

Phys. Rev. D68, 085015

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

**Alessandro Codello and Roberto Percacci (2008)**

Fixed Points of Nonlinear Sigma Models in d>2.

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

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
Yukawa Systems.

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
systems.

Acta Phys. Polon. supp. , 541 (2009)

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
Thirring model

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
model

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.*

Asymptotic safety and the SU(N) gauged nonlinear
sigma model

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.

An alternative view on the electroweak interactions

**Xavier Calmet
(2010b)**

Asymptotically safe weak interactions

The electroweak S and T parameters from a fixed
point condition

Phys. Rev. Lett. 107
021803 (2011)

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

Fermions and Goldstone bosons in an
asymptotically safe model

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

**Daniel Litim, Roberto Percacci and Leslaw
Rachwal (2011)**

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

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

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

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

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

**Eur.Phys.J. C73 (2013) 2652**

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

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

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

MCRG flow for nonlinear sigma model

**PoS LATTICE2013 (2013) 052**

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

**Daniel
Litim and Francesco Sannino (2014)**

Asymptotic
safety guaranteed.

JHEP 1412 (2014) 178

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

**Francesco
Sannino and Ian M. Shoemaker (2014)**

Phys.Rev. D92 (2015) no.4, 043518

arXiv:1412.8034 [hep-th]

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

Asymptotic safety in the sine-Gordon model

**Daniel
Litim and Francesco Sannino (2015)**

Vacuum
stability of asymptotically safe gauge-Yukawa theories

JHEP 1601 (2016) 081

**Holger
Gies and Luca Zambelli (2015)**

Asymptotically
free scaling solutions in non-abelian Higgs models.

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

Inflation
from asymptotically safe theories

Phys.Rev. D91 (2015) 103521

Asymptotic
Safety in the Conformal Hidden Sector?

J.Phys. G45 (2018) no.9, 095002

**Andrew
Bond and Daniel Litim (2016) **

Theorems
for asymptotic safety of gauge theories

Eur.Phys.J. C77 (2017) no.6, 429

Thermodynamics of asymptotically safe theories

Phys.Rev. D92 (2015) no.6, 065014

**Borut
Bajc and Francesco Sannino (2016)**

Asymptotically
safe Grand Unification

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

Naturalness
of Asymptotically safe Higgs

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

Directions
for model building from asymptotic safety

JHEP 1708 (2017) 004

**Steven
Abel and Francesco Sannino (2017)**

Radiative
symmetry breaking from interacting UV fixed points

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

Phys.Rev. D97 (2018) no.9, 095013

arXiv:1708.00437 [hep-th]

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

Asymptotically
safe Standard Model via vector-like fermions

More
asymptotic safety guaranteed

Phys.Rev. D97 (2018) no.8, 085008

Asymptotic
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

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

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

UV conformal window for asymptotic safety

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

Asymptotic
safety of scalar field theories

Price
of asymptotic safety

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

Asymptotically safe extensions of the Standard Model with flavour phenomenology

arXiv:1905.11020 [hep-th]**Borut
Bajc, Adrian Lugo and Francesco Sannino (2019)**

Safe
hologram

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

symptotic safety with Majorana fermions and new large N equivalences

arXiv:1911.11168 [hep-th]**
Classic papers on quantum gravity**

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

One loop divergencies in the
theory of gravitation.

Annales
Poincare Phys.Theor.A20, 69-94

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

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

Nonrenormalizability
of the Quantized Einstein-Maxwell System

Phys. Rev.
Lett.32 245-247

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

Nonrenormalizability
of quantized fermion-gravitation interactions

Lett. Nuovo
Cim. 11, 218-220

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

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

Phys.
Lett. 50B, 491

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

One Loop
Divergences of Quantized Einstein-Maxwell Fields

Phys. Rev. D10, 401

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

Nonrenormalizability
of the Quantized Dirac-Einstein System

Phys. Rev.
D10, 411

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

One Loop
Divergences of the Einstein Yang-Mills System

Phys. Rev.
D10, 3337

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

**Kellogg
S. Stelle (1977)**

Renormalization of
higher--derivative gravity.

Phys. Rev.
D 16, 953-969.

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

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

One Loop
Finiteness Of Quantum Gravity
Off Mass Shell.

Nucl. Phys.
B137, 145-163

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

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

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

Yad.Fiz.39,
998-1010

**E.
Tomboulis (1977)**

1/N
expansion and renormalizability in quantum gravity

Phys.
Lett. 70 B, 361.

**E.
Tomboulis (1980).**

Renormalizability and asymptotic
freedom in quantum gravity.

Phys.
Lett. B 97, 77.

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

**Marc H.
Goroff, Augusto Sagnotti (1986)**

The Ultraviolet Behavior of
Einstein Gravity.

Nucl. Phys. **B266** 709

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

**Anton E.M. van de Ven (1992)**

Two loop
quantum gravity.

Nucl. Phys.
B378, 309-366

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

**J. Julve, M. Tonin (1982)**

Quantum Gravity with Higher
Derivative Terms.

Nuovo Cim. **B46**, 137-152

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

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

Renormalizable Asymptotically Free Quantum Theory
Of Gravity.

Phys.Lett. **B104,** 377-381

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

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

Nucl. Phys. **B 201**, 469.

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

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

Asymptotic freedom in
higher--derivative quantum gravity.

Phys. Lett. 159B, 269

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

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

Conformal quantum gravity
with the Gauss-Bonnet term.

**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
theory

Phys. Lett. B 632 (2006) 433

**B. Holdom and J. Ren (2015)**

QCD analogy for quantum
gravity

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)

Space-Time Foam.

Nucl. Phys. B144,
349-362

S.W. Hawking (1978b)

Euclidean Quantum Gravity.

Cargese Summer Inst. 1978, 0145

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

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

Quantizing Gravitational Instantons.

Nucl. Phys. B146, 90

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

Path Integrals and the
Indefiniteness of the Gravitational Action.

Nucl. Phys. B138, 141

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

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

The Propagation Of Particles In Space-Time Foam.

Phys. Lett. B86, 175-178

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

New Gravitational Index
Theorems and Supertheorems.

Nucl. Phys. B154:301

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

Quantizing Gravity with a Cosmological Constant.

Nucl. Phys. B170, 480

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

**H. Lu and C. Pope
**Critical gravity in four dimensions

Phys.Rev.Lett. 106 (2011) 181302

arXiv:1101.1971 [hep-th]

**Effective field theory of gravity
**

**John F. Donoghue (1994a)**

Leading quantum correction to the Newtonian
potential.

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

**John F. Donoghue (1994b)**

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

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

** H.W. Hamber and Liu (1995)**

On the quantum corrections to the Newtonian
potential.

Phys. Lett. B357, 51

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

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

Gravitational interaction to one loop in
effective quantum gravity.

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

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

**John F. Donoghue (1995)**

Introduction to the effective
field theory description of gravity.

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

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

Leading quantum gravitational
corrections to scalar QED.

Phys. Rev. D66, 084023

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

Quantum power correction to the Newton law.

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

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

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

Quantum corrections to the Schwarzschild and Kerr
metrics.

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

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

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

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

Phys. Rev. D 67, 084033

[Erratum-ibid. D 71 (2005) 069903

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

Cliff P. Burgess (2004)

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

http://www.livingreviews.org/lrr-2004-5

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

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

Quantum long range interactions in general
relativity.

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

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

**G.G. Kirilin (2007)**

Quantum corrections to the Schwarzschild metric
and reparametrization transformations.

Phys. Rev. D75, 108501

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

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

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

Phys. Rev. D75, 108502

A detailed reply to the criticism in Kirilin (2007)

D. Espriu and D. Puigdomenech (2009)

Gravity as an effective field theory

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

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

Low energy quantum Gravity from the Effective
Average Action

Phys. Rev. D82, 084011 (2010)

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

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

Solving the Effective Field Equations for the
Newtonian Potential

Class. and Quantum Grav. 27, 2450008 (2010)

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

**John F. Donoghue (2012)**

The effective field theory treatment of quantum
gravity

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

**John F. Donoghue (2016a)**

Is the spin connection
confined or condensed?

**John F. Donoghue (2016b)**

A conformal model of
gravitons

**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.*

The semiclassical limit of
causal dynamical triangulations.

Nucl. Phys. B894, 144-165 (2011)

J. Laiho and D. Coumbe (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
principle.
*

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.

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

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

Status of
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

**Gravitational effects on matter couplings**

L. Griguolo and R. Percacci (1995)

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

Phys. Rev. D 52, 5787 (1995).

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
Gauge Couplings.

Commun. Theor. Phys. 54, 1040 (2010)

These authors use a regularization method that preserves
gauge invariance while not

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,

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
interactions.

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
quantum gravity

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

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

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

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

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)

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

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

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
kinematical identity.
*

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
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