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.
In these two papers, the beta function of Newton’s constant is computed using the ε expansion around two dimensions.
Steven
Weinberg (1979)
Ultraviolet
divergences in quantum theories of gravitation.
In "General Relativity: An Einstein centenary
survey", ed. S. W. Hawking and W. Israel, chapter 16,
pp.790--831; Cambridge University Press.
The
term "Asymptotic Safety" was introduced in this paper to
characterize a class of theories that have a good
ultraviolet limit and are predictive. The condition for this
to happen is that there exists a fixed point with finitely many UV
attractive directions. Based on results of the ε expansion
around two dimensions, it was suggested that gravity may be
asymptotically safe.
Lee
Smolin (1982)
A
fixed point for quantum gravity.
Nucl.
Phys. B 208, 439-466
It
was shown in this paper that a fixed point must exist in 4-d
gravity in the leading order of a 1/N approximation.
Hikaru
Kawai and Masao Ninomiya (1990)
Renormalization
group and quantum gravity.
Nuclear
Physics B 336, 115-145
This
paper discusses several issues related to the application of
the renormalization group to quantum gravity, in particular
in relation to the ε expansion. It is
observed that due to its nontrivial dimensionality, the
running of
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
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 R2 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 R2 is computed starting
from the Einstein-Hilbert truncation of the action. The
contribution of the coupling η to its own beta function is
not taken into account.
Sven
Falkenberg, Sergei D. Odintsov (1998)
Gauge
dependence of the effective average action in Einstein
gravity.
Int.
J. Mod. Phys. A13, 607-623
Talk
given at the 8th Marcel Grossmann Meeting.
Wataru
Souma (1999)
Nontrivial
ultraviolet fixed point in quantum gravity.
Prog.
Theor. Phys. 102, 181.
The
beta functions of Reuter 1998 are solved numerically and a
nontrivial fixed point is found. It is shown that it is UV
attractive in both directions.
Wataru
Souma (2000)
Gauge
and cutoff function dependence of the ultraviolet fixed point
in quantum gravity.
Martin
Reuter (2000)
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 R2 (where η is a dimensionless coupling). The standard De
Donder gauge is used with α=1. It is found
that the nontrivial fixed point still exists, with values of
the cosmological constant and
Oliver
Lauscher and Martin Reuter (2002c)
Is
quantum Einstein gravity nonperturbatively renormalizable?
Class.
Quant. Grav. 19, 483.
A
summary of then-current evidence for asymptotic safety.
Martin
Reuter, Frank Saueressig (2002b)
A
Class of nonlocal truncations in quantum Einstein gravity and
its renormalization group behavior.
Phys.
Rev. D66, 125001
Contains
an analysis of actions that contain the Einstein-Hilbert
term plus function of the volume.
Roberto
Percacci and Daniele Perini (2002)
Constraints
on matter from asymptotic safety.
Phys.
Rev. D67, 081503 (R).
It
is shown that the existence of a FP can place constraints on
the type and number of matter fields. Gravity is
treated in the Einstein-Hilbert truncation and the matter
fields are minimally coupled. The fermions are treated by
imposing a so-called "type I" cutoff on the square of the
Dirac operator. This gives rise to issues that are discussed
in Dona' and Percacci 2012.
Peter
Forgacs, Max Niedermaier (2002)
A
Fixed point for truncated quantum Einstein gravity.
Max
Niedermaier (2002)
On
the renormalization of truncated quantum Einstein gravity.
JHEP
0212, 066
Instead
of keeping all the degrees of freedom of the metric and truncating the
action, in these papers gravity is simplified by
considering only metrics with two Killing vectors, while
retaining the most general action. Asymptotic
safety of the resulting theory is discussed.
Roberto
Percacci and Daniele Perini (2003)
Asymptotic
safety of gravity coupled to matter.
Phys.
Rev. D68, 044018 .
Same
general setup as Percacci and Perini 2002, but here one
scalar field is allowed to have arbitrary
potential
V and interactions F R where F is a function of the
scalar field. It is observed that there are models with
nontrivial V and F where all scalar interactions are
asymptotically free. The formulae for the beta functions
contain many misprints. For correct and more explicit
formulae see the appendix of Narain and Percacci 2009b.
Max
Niedermaier (2003)
Dimensionally
reduced gravity theories are asymptotically safe.
Nucl.
Phys. B 673, 131-169.
Martin
Reuter, Frank Saueressig (2004)
Nonlocal
quantum gravity and the size of the universe.
Fortsch.
Phys. 52, 650-654
Talk
given at 36th International Symposium Ahrenshoop on the
Theory of Elementary Particles: Recent Developments in
String M Theory and Field Theory, Wernsdorf, Germany, 26-30
Aug 2003.
Daniel
F. Litim (2004)
Fixed
points of quantum gravity.
Phys.
Rev. Lett. 92, 201301.
By
means of a clever choice of cutoff function, closed
expressions are given for the beta functions of the
cosmological constant and
Roberto
Percacci and Daniele Perini (2004)
On
the ultraviolet behaviour of Newton's constant.
Class.
and Quantum Grav. 21, 5035.
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
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,
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 R2 and Weyl2 terms. No
further approximation is made. Unlike in the one loop
approximation, the couplings that multiply the higher
derivative terms are not asymptotically free, but have
finite limits. Two of the critical exponents are very close
to the results of the Einstein-Hilbert truncation; the other
two are rather large and have opposite signs. The critical
surface is therefore three dimensional.
Dario
Benedetti, Pedro F. Machado and Frank Saueressig (2009b)
Taming
perturbative divergences in asymptotically safe gravity
Nucl.
Phys. B824, 168-191 (2010).
In
this paper the setup is similar to the previous one, but
there is an additional minimally coupled scalar field. The
reason why this is significant is that the appearance of
curvature squared divergences in Einstein theory at one
loop, in the presence of a scalar field, signals
nonrenormalizability(‘t Hooft and Veltman). By proving that
this truncation admits a nontrivial fixed point, the authors
show that nonrenormalizable divergences have no effect on
the behavior of the RG flow, as seen using nonperturbative
tools.
Steven
Weinberg (2009a)
Living
with infinities.
Reviews
in a historical perspective the problem of infinities in
quantum field theory, and how it may be resolved by
asymptotic safety.
Martin
Reuter and Holger Weyer (2008b)
The
role of Background Independence for Asymptotic Safety in
Quantum Einstein Gravity.
Gen.
Rel. Grav. 41, 983-1011 (2009)
Talk
given by M.R. at the WE-Heraeus-Seminar "Quantum Gravity:
Challenges and Perspectives", Bad Honnef, April 14-16, 2008
Pedro
F. Machado and Roberto Percacci (2009)
Conformally
reduced quantum gravity revisited.
Phys.
Rev. D80, 024020
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)
Gaurav
Narain and Roberto Percacci (2009b)
Gaurav
Narain and Christoph Rahmede (2009)
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)
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)
This paper addresses basic issues regarding the derivation of the functional RG equation, taking as a starting point the functional integral on phase space rather than the functional integral over configuration space. The reason for listing it here is that the most striking consequence of this approach would be a quadratic rather than quartic running of the vacuum energy. In addition, the "reconstruction problem" of the bare action is addressed.
Dario Benedetti and Simone Speziale (2011)
Perturbative
quantum gravity with the Immirzi parameter.
JHEP 1106, 107 (2011)
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)
This article is devoted to an analysis of the gauge parameter dependence of the beta functions. By means of various technical improvements, the author manages to separate the on shell part of the calculation in a clean way, showing that it is gauge-parameter independent to all orders in the cosmological constant, as expected.
Max
Niedermaier (2011)
Can
a nontrivial gravitational fixed point be identified in
perturbation theory?
Alessandro Codello (2011)
Large N quantum gravity
New J. of Phys. 14, 015009 (2012)
Astrid Eichhorn (2011)
Observable
consequences of quantum gravity: can light fermions exist?
J. Phys. Conf. Ser. 360, 012057 (2012)
Talk given at Loops'11, Madrid, to appear in J. of Phys. Conf Ser.
Martin Reuter and Frank Saueressig (2011)
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.
In the proceedings of the conference "Time and matter" Budva, Montenegro, October 2010.
Roberto Percacci (2011b)
RG
flow of Weyl-invariant dilaton gravity.
New J. of Phys. 13, 125013 (2011)
It is shown here that the RG flow can be constructed in such a way as to preserve Weyl invariance, when a dilaton is present.
Frank Saueressig, Kai Groh, Stefan Rechenberger and Omar Zanusso (2011)
Higher
derivative gravity from the universal renormalization group
machine
PoS EPS-HEP 2011 124 (2011)
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
The phase diagram of quantum gravity from
diffeomorphism invariant RG flows
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]
This paper addresses two issues that arise when gravity is coupled to fermions: the first is the sign of the fermionic contribution to the running of Newton's constant, the second is the difference between the gravitational beta functions in metric and tetrad formalism. It is common practice to compute the one loop fermionic effective action as one half the trace of the logarithm of the square of the Dirac operator. When a cutoff is imposed on the square of the Dirac operator, the sign of the beta functions differs when one uses a cutoff that depends on -Box (type I) or on the square of the Dirac operator -Box+R/4 (type II). To decide which one of these gives the right result, the beta function is computed using a spectral sum, with the cutoff imposed directly on the Dirac operator (rather than its square). This agrees with the type II cutoff. Arguments are then given for why the type I cutoff should have been avoided in the first place.
Astrid Eichhorn (2012)
Experimentally testing asymptotically safe quantum gravity with photon-photon scattering
Talk given at the 13th Marcel Grossmann meeting (Stockholm, july 2013)
Alessandro Codello, Giulio d'Odorico, Carlo Pagani and Roberto Percacci (2012)
Renormalization
group and Weyl invariance.
Class.Quant.Grav. 30 (2013) 115015
The main result of this paper is a general proof that when one quantizes a classically Weyl invariant system in the presence of a dilaton, one can construct an effective action that is also Weyl invariant. This is proven by constructing a flow that is Weyl invariant. The construction is given first for non-interacting matter coupled to external gravity and then extended to interacting matter and dynamical gravity. Even though Weyl invariance remains unbroken, the trace anomaly is present as usual. Some explicit calculations of Weyl-invariant effective actions are given in two and four dimensions. Various issues are addressed, such as the meaning of a cutoff in a conformal theory, or the notion of flow in a space of conformal theories.
S. Nagy (2012)
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
Based on the general properties of the flow equation for f(R) (in a slightly different form from the one of Benedetti and Caravelli 2012) it is shown that if a scaling solution exists, it must have a finite number of relevant perturbations.
K. Falls, D. Litim, K. Nikolakopulos and C. Rahmede (2013)
A
bootstrap towards asymptotic safety
Jan-Eric Daum, Martin Reuter (2013)
Einstein-Cartan
gravity, asymptotic safety and the running Immirzi parameter
Annals Phys. 334 (2013) 351-419
A detailed account of the calculations in Daum and Reuter (2010a).
R. Percacci, C. Pope, M. Perry and E. Sezgin (2013)
Beta
functions of topologically massive supergravity
JHEP 1403 (2014) 083
Extends previous paper by Percacci and Sezgin to include fermionic contributions. Calculations are done both on the sphere (positive cosmological constant) and hyperboloid (negative cosmological constant).
Alfio
Bonanno, Martin Reuter (2013)
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
In this paper the anomalous dimension of the graviton and ghost are calculated from the respective two-point functions. When the result is inserted in the flow equations for the Einstein-Hilbert truncation a nontrivial fixed point is found, with very small and negative cosmological constant, and real scaling exponents.
Probing the quantum nature of
spacetime by diffusion
Phys.Rev. D87 (2013) 12, 124028
Juergen A. Dietz and Tim R. Morris (2013)
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
Revisits the calculation of the beta functions in higher derivative gravity. The main new result is the extension to dimensions different than four. The cases three, five and six are discussed in some detail. Due to differences in the heat kernel coefficients, the results do not agree with previous calculations of de Berredo Peixoto and Shapiro in 4+epsilon dimensions.
Dario Benedetti and Filippo Guarnieri (2013)
Brans-Dicke
theory in the local potential approximation
New J.Phys. 16 (2014) 053051
This is a study of the flow equations for the scalar potential in Brans-Dicke-theory, motivated in part by the classical equivalence of the f(R) theory and scalar-tensor theory. Only the case when the Brans-Dicke parameter is equal to zero is studied in detail. The fixed point equation for the potential is derived in two different gauges and solutions are found to be very different in the two cases. The inconsistency is attributed to the restriction on the Brans-Dicke parameter.
Pietro Dona', Astrid Eichhorn and Roberto Percacci (2013)
Matter
matters in asymptotically safe quantum gravity
Phys.Rev. D89 (2014) 084035
As in QCD too many fermions spoil asymptotic freedom, it is conceivable that in quantum gravity too many matter fields could spoil asymptotic safety. This issue is addressed under the following approximations: the Einstein-Hilbert truncation for gravity but retaining a nontrivial wave function renormalization for the graviton and ghost; minimal coupling for matter, neglecting all self interactions but keeping track of the wave function renormalization. The main novelty are the matter contribution to the gravitational anomalous dimension and the gravitational contribution to the matter anomalous dimension. For a given number of gauge fields there is a finite number of allowed combinations of scalar and fermion fields.
Carlo Pagani and Roberto Percacci (2013)
Quantization
and fixed points of non-integrable Weyl theory
Class. Quant. Grav. 31 (2014) 115005
Complementing earlier results on integrable Weyl theory, here the RG flow is derived for a Weyl invariant theory containing the metric, a scalar field and Weyl's gauge field. Special attention is payed to the relation between the cases when the scalar is massive and massless.
Maximilian Demmel, Stefan Rechenberger and Omar Zanusso (2014)
RG
flows of Quantum Einstein Gravity on maximally symmetric
spaces
JHEP 1406 (2014) 026
arXiv:1401.5495
[hep-th]
A
study of the flow equation for conformally reduced f(R)
gravity in three dimensions. Two scaling solutions are
found.
Nicolai Christiansen, Jan Pawlowski and Andreas Rodigast (2014)
Global
flows in quantum gravity
Phys.Rev. D93 (2016) no.4, 044036
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
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
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]
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
The first part of this paper contains a review of known scaling relations of two-dimensional quantum gravity. In the second part the scaling exponents are calculated using the functional RG, both in 2 dimensions (where the flow is driven by the Polyakov action) and 2+epsilon dimensions (where it is driven by the Hilbert term). The known correct result of the central charge -25 is only reproduced if one uses the exponential parametrization.
Maximilian Demmel, Frank Saueressig and Omar Zanusso (2014)
RG
flows of Quantum Einstein Gravity in the linear-geometric
approximation
Annals
Phys. 359 (2015) 141-165
arXiv:1412.7207
[hep-th]
Roberto Percacci and Gian Paolo Vacca (2015a)
Search
of scaling solutions in scalar-tensor gravity
Eur.Phys.J. C75 (2015) 5, 188
arXiv:1501.00888
[hep-th]
The flow equation for a scalar-tensor theory of type V-FR is written using the exponential parametrization of the metric and a "physical unimodular" gauge, where the trace and spin one components of the metric fluctuation are put to zero. In this gauge there is no undifferentiated potential appearing in the hessian, so that the flow is free of IR singularities. The resulting flow equations are much simpler than those of Narain and Percacci (2009b). Besides the "Gaussian matter fixed point" with constant V and F, there is, in any dimension d>2, a nontrivial solution with constant V and quadratic F. In d=3 there is evidence for an analog of the Wilson-Fisher fixed point, but no proof of global existence is given.
Kevin
Falls (2015)
On
the renormalization of Newton's constant
Phys.Rev. D92 (2015) no.12, 124057
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]
The paper illustrates the use of Chebyshev polynomial in the solution of functional fixed point equations. It gives a complete solution for the equations of arXiv:1501.00888 [hep-th], in three dimensions.
Is there a C-function in 4d quantum Einstein
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]
The results of Percacci and Vacca (2015) are generalized to the case of an N-plet of scalar fields. For N>2 there is an additional solution in closed form.
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]
The flow equation for f(R) gravity is written in exponential parametrization and physical gauge. As in Demmel, Saueressig and Zanusso, the cutoff depends on some parameters, the coefficients of the endomorphism in the operator used to construct the cutoff. There are discrete choices of the parameters for which the equation admits a quadratic solution. When the parameters change continuously, the solution seems also to change continuously, at least in polynomial truncation.
Tim R. Morris and Zoe H. Slade (2015)
Solutions to the reconstruction problem in asymptotic safetyHolger
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)
Essential nature of Newton's constant in unimodular gravityNobuyoshi Ohta, Roberto Percacci and Gian Paolo Vacca (2015a)
Renormalization
Group Equation and scaling solutions for f(R) gravity in
exponential parametrization
European Physical Journal C (2016) 76:46
arXiv:1511.09393
[hep-th]
More details are given of the solutions found in the preceding paper. In addition, numerical solutions are studied for selected values of the endomorphism parameters.
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)
The Gravitational Two-Loop Counterterm is Asymptotically Safe
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)
Manifestly diffeomorphism invariant classical Exact Renormalization GroupPeter Labus, Tim R. Morris and Zoe H. Slade (2016)
Background independence in a background dependent renormalization groupAstrid Eichhorn, Aaron Held and Jan Pawlowski (2016)
Quantum
gravity effects on a Higgs-Yukawa model
Phys.Rev. D94 (2016) no.10, 104027
arXiv:1604.02041
[hep-th]
Nobuyoshi Ohta, Roberto Percacci and Antonio Duarte Pereira (2016a)
Gauges
and functional measures in quantum gravity I: Einstein
theory
JHEP 1606 (2016) 115
arXiv:1505.00454
[hep-th]
This paper contains a general computation of the off-shell one-loop divergences in Einstein gravity on the sphere, using a two-parameter family of path integral measures, corresponding to different ways of parametrizing the graviton field, and a two-parameter family of gauges. Trying to reduce the gauge- and measure-dependence selects certain classes of measures and gauges respectively. There is a choice of two parameters (corresponding to the exponential parametrization and the partial gauge condition that the quantum field be traceless) that automatically eliminates the dependence on the remaining two parameters and on the cosmological constant. It is observed that the divergences are invariant under a Z_2 "duality" transformation that (in a particularly important special case) involves the replacement of the densitized metric by a densitized inverse metric as the fundamental quantum variable. This singles out a formulation of unimodular gravity as the unique "self-dual" theory in this class.
Tobias Henz, Jan Pawlowski and Christoph Wetterich (2016)
Scaling
solutions for Dilaton Quantum Gravity
Phys.Lett. B769 (2017) 105-110
Jurgen Dietz, Tim R. Morris and Zoe H. Slade (2016)
Fixed point structure of the conformal factor field in quantum gravityNobuyoshi Ohta and Kevin Falls (2016)
Renormalization
Group Equation for f(R) gravity on hyperbolic spaces
Phys.Rev. D94 (2016) no.8, 084005
arXiv:1507.08460
[hep-th]
This paper extends previous work of Ohta et al from the case of compact to non-compact background. It is found that the polynomial expansion does not yield stable result as the truncation is extended.
Quantum
gravity on foliated spacetime - asymptotically safe and
sound
Phys.Rev. D95 (2017) no.8, 086013
Tim R. Morris (2016)
Large curvature and background scale independence in single-metric approximations to asymptotic safetyNobuyoshi Ohta, Roberto Percacci and Antonio Duarte Pereira (2016b)
Gauges
and functional measures in quantum gravity II: higher
derivative gravity
Eur.Phys.J. C77 (2017) no.9, 611
arXiv:1610.07991
[hep-th]
The analysis of OPP (2016a) is extended to the case when the action contains Ricci squared and Ricci scalar squared terms. The background is assumed to be Einstein. The York decomposition is used in conjunction with Lichnerowicz Laplacians. The results are very similar, in particular the duality is found also in this case.
Astrid Eichhorn and Stefan Lippoldt (2016)
Quantum gravity and standard model-like fermionsCarlo Pagani and Martin Reuter (2016)
Composite operators in asymptotic safetyRoberto
Percacci and Gian Paolo Vacca (2016)
The background scale Ward identity in quantum gravity
Eur.Phys.J. C77 (2017) no.1, 52
arXiv:1611.07005
[hep-th]
This paper follows Morris (2016) but with three differences at the technical level: the exponential parametrization of the metric, a higher-derivative gauge fixing and a "pure" cutoff. It is shown that with these modifications the anomalous terms in the scale Ward identity (recall that the classical action is background scale invariant) is equal to the r.h.s. of the flow equation, in any dimension.
Nicolai Christiansen (2016)
Four-derivative
quantum gravity beyond perturbation theory
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)
Asymptotic safety of higher derivative quantum gravity non-minimally coupled with a matter systemSergio Gonzales-Martin, Tim R. Morris and Zoe H. Slade (2017)
Asymptotic solutions in asymptotic safetyW.B. Houthoff, A. Kurov and Frank Saueressig (2017)
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
Astrid Eichhorn (2017)
Status of the asymptotic safety paradigm for quantum gravity and matterUpper
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)
Nonminimal hints for asymptotic safetyNicolai 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)
Quantum gravity predictions for the fine-structure constantNicolai 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)
Quantum gravity fluctuations flatten the Planck-scale Higgs potentialSumarna 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)
Renormalization group properties in the conformal sector: towards perturbatively renormalizable quantum gravityAstrid Eichhorn, Aaron Held and Peter Vander Griend (2018)
Asymptotic safety in the darkNatalia Alkofer and Frank Saueressig (2018)
Asymptotically safe f(R)-gravity coupled to matter I: the polynomial case
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)
Effective universality in quantum gravityMatthew P. Kellett, Tim R. Morris (2018)
Renormalization group properties of the conformal mode of a torusCarlo Pagani and Martin Reuter (2018)
Finite Entanglement Entropy in Asymptotically Safe Quantum GravityTowards
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)
Asymptotically safe f(R)-gravity coupled to matter II: global solutions
Simon Friederich (2018)
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)
How perturbative is quantum gravity?Astrid Eichhorn (2018)
An asymptotically safe guide to quantum gravity and matterJan.M. Pawlowski, Manuel Reichert, Christof Wetterich, Masatoshi Yamada (2018)
Higgs scalar potential in asymptotically safe quantum gravity
Gustavo P. De Brito, Yuta Hamada, Antonio D. Pereira,
Masatoshi Yamada (2019)
Christof Wetterich (2019)
Quantum scale symmetryChristof Wetterich, Masatoshi Yamada (2019)
Variable Planck mass from gauge invariant flow equationCarlo
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)
Asymptotic safety, string theory and the weak gravity conjectureGustavo P. De Brito, Astrid Eichhorn, Antonio D. Pereira (2019)
A link that matters: towards phenomenological tests of unimodular asymptotic safetyJohn
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 discusses the existence of inflationary
(exponential or power law) cosmological solutions in a class
of renormalization group improved polynomial f(R) theonly
with matter. The nonconservation of the energy momentum
tensor is also discussed.
B.F.L.
Ward (2010a)
An
estimate of \Lambda in Resummed Quantum Gravity in the context
of asymptotic safety
Roberto
Casadio, Stephen Hsu and Behrouz Mirza (2010)
Asymptotic
safety, singularities and gravitational collapse
Phys. Lett. B695, 317-319 (2011)
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)
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)
In this paper the cutoff is allowed to depend on time and the energy momentum tensor is assumed to be conserved. This put constraints on the form of the cutoff. The field equations and the RG equations are written as a coupled autonomous system. Various classes of solutions of these equations are discussed.
Changrim Ahn, Chanju Kim and Eric V. Linder (2011)
From
asymptotic safety to dark energy
Phys. Lett. B704 10-14 (2011)
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)
Sungwook E. Hong, Young Jae Lee, Heeseung Zoe (2011)
The
Possibility of Inflation in Asymptotically Safe Gravity
Alfio Bonanno (2012)
An
effective action for asymptotically safe gravity
Phys.Rev. D85 (2012) 081503
It is argued that the so called "RG improvement" i.e. the replacement of the cutoff scale k by a physical parameter of the problem, should be performed in the action, rather than the equations of motion. This is in line with examples from QCD. It is assumed that the cutoff is proportional to the square root of R. When substituted in the Einstein-Hilbert action this leads to a kind of f(R) theory. This is analyzed in the vicinity of the fixed point, the flow can be solved by linearization and consists of spiralling trajectories. The effective theory contains a term of the form cos log R. It is shown that there exist infinitely many de Sitter solutions, some being stable and others unstable. In particular there are unstable solutions with sufficient e-foldings to produce inflation.
Mark Hindmarsh and Ippocrates Saltas (2012)
f(R)
gravity from the renormalisation group
Phys.Rev. D86 (2012) 064029
As in the preceding paper, the cutoff is identified with the square root of R in the action, up to a factor r. The resulting theory is then analyzed by going to the Einstein frame. As in the preceding paper, infinitely many de Sitter solutions are found. In the Lambda-G plane, the evolution of the universe would correspond to the piece of RG trajectory that starts from an "outer" de Sitter solution in the UV (i.e. in the past, producing inflation), passes near the Gaussian fixed point and then approaches another de Sitter point (accelerated expansion). Viability of the picture in the classical regime requires r near one, but this would lead to excessive primordial fluctuations. Viability of the inflationary phase requires a large r. It is suggested that this discrepancy may be solved in the presence of additional degrees of freedom.
Babette Dobrich and Astrid Eichhorn (2012)
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
This paper elaborates the prediction of a Higgs boson near the lower mass bound, originally presented in Shaposhnikov and Wetterich (2009). Three loop beta functions are used for the low energy domain. Asymptotic safety arguments are used to predict the Higgs mass to be 129 +/- 6 GeV. It is argued that the discovery of a Higgs with this mass would point towards the absence of intermediate scales between the Fermi and the Planck scale, and may actually point towards a connection between the two.
Christopher Estrada and Matilde Marcolli (2012)
Asymptotic
safety, hypergeometric functions and the Higgs mass in
spectral action models
Int.J.Geom.Meth.Mod.Phys. 10 (2013) 1350036
arXiv:1208.5023
[hep-th]
On
antiscreening in perturbative quantum gravity and resolving
the Newtonian singularity
Chao Fang and Quin-Guo Huang (2012)
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
This paper deals with effective actions of the form R+R^2. The beta functions are shown to have a nontrivial fixed point where the R^2 term is asymptotically free (as in one-loop calculations). It is shown that there are RG trajectories that describe well Starobinski inflation. In particular the value of the R^2 coupling at the Planck scale is determined from CMB data. It is shown to be of order 10^(-9).
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
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.
Xavier Calmet
(2010b)
Asymptotically safe weak interactions
The electroweak S and T parameters from a fixed
point condition
Phys. Rev. Lett. 107
021803 (2011)
Fermions and Goldstone bosons in an
asymptotically safe model
Daniel Litim, Roberto Percacci and Leslaw Rachwal (2011)
Scale-dependent Planck mass and Higgs VEV from
holography and functional renormalization
The system being studied here is the nonlinear sigma
model coupled to gravity. It is shown that there is a
nontrivial fixed point in the simplest truncation,
involving only two-derivative terms both for gravity
and for the scalars. The results of the functional RG
are surprisingly similar to those of a "holographic"
RG based on five-dimensional AdS space, possibly
containing source brane a la Randall-Sundrum.
Raphael Flore, Andreas Wipf and Omar Zanusso (2012)
Functional renormalization group of the
non-linear sigma model and the O(N) universality class
Holger Gies, Stefan Rechenberger, Michael Scherer and Luca Zambelli (2011)
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
Daniel
Litim and Francesco Sannino (2014)
Asymptotic
safety guaranteed.
JHEP 1412 (2014) 178
Francesco
Sannino and Ian M. Shoemaker (2014)
J. Kovacs, S. Nagy, and K. Sailer (2014)
Asymptotic safety in the sine-Gordon model
Daniel
Litim and Francesco Sannino (2015)
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
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)
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
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)
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.
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)
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
predict the value of the fine structure constant.
Quantum gravitational
contributions to the beta function of quantum
electrodynamics.
Phys. Lett. B700, 86-89 (2011)
Andreas Rodigast and Theodor Schuster (2011)
Gravitational corrections to non gauge
interactions.
Nucl. Phys. Proc. Suppl. 216, 263-264 (2011)
Proceedings of "String Theory: Formal Developments And Applications" 21 Jun - 3 Jul 2010, Cargese, France
On the running of the
gravitational constant
J.C.C. Felipe, L.A. Cabral, L.C.T. Brito, M. Sampaio and M.C. Nemes (2011)
Ambiguities in the
gravitational correction of quantum electrodynamics.
Hao-Ran Chang,
Wen-Tao Hou and Yi Sun (2012)
Gravitational corrections to phi^4 theory with
spontaneously broken symmetry
Artur R. Pietrykowski (2012)
Interacting scalar fields in the context of
effective quantum gravity
G. Narain and R. Anishetty (2012)
Charge renormalization due to graviton loops
JHEP 1307 (2013)
106
G. Narain and R. Anishetty (2013)
Running couplings in quantum theory of gravity
coupled to gauge fields
JHEP 1310 (2013)
203
S. Gonzales-Martin and C.P.
Martin (2017)
Do the gravitational
corrections to the beta functions of the quartic and
Yukawa couplings have an intrinsic physical meaning?
Sigurd Sannan (1986)
Gravity as the limit of the type-II superstring
Phys. Rev. D34, 1749 (1986)
This paper contains explicit formulae for the three- and
four-point graviton vertices and scattering amplitudes.
Z. Bern, S.K. Blau and E. Mottola (1991)
General covariance of the path integral fro quantum gravity.
Phys. Rev. D43, 1212 (1991)
E. Mottola (1995)
Functional integral over geometries.
J. Math. Phys. 36, 2470 (1995)
These two papers present a geometrical
definition of the gravitational path integral measure
that is alternative to the standard Fadeev-Popov
construction.
A.O. Barvinsky, A.Yu. Kamenshchik, I.P. Karmazin (1993)
The Renormalization group for nonrenormalizable theories: Einstein gravity with a scalar field.
Phys. Rev. D48, 3677-3694
Discuss the renormalization of a general class of
theories of scalars coupled to gravity.
Roberto Floreanini and Roberto Percacci (1995a)
Average effective potential for the conformal factor.
Nucl. Phys. B 436, 141-160.
Roberto Floreanini and Roberto Percacci (1995b)
Renormalization--group flow of the dilaton potential.
Phys. Rev. D 52, 896-911.
Roberto Floreanini and Roberto Percacci (1995c)
The heat kernel and the average effective potential.
Phys. Lett. B 356, 205-210.
These three papers contain early (pre-ERGE) application
of the RG to gravity.
They deal with the potential for the conformal factor
of the metric and its RG flow. In the ERGE setup, such
potentials appear in the coarse-grained affective
action, which depends on two metrics: the backgound
metric and the classical metric introduced in the Legendre
transform.
E.T. Tomboulis (1996)
Exact relation between Einstein and quadratic quantum gravity
Phys. Lett. B389, 225-230
arXiv: hep-th/9601082
Writes the transformation of the metric which eliminates R2 and Ricci2 terms, at the expense of introducing scalar fields.
M.Yu. Kalmykov (1998)
Manifestation of metric renormalization in quantum R**2 gravity.
Discusses the necessity of renormalizing the metric.
Damiano Anselmi (2003)
Absence of higher derivatives in the renormalization of propagators in quantum field theories with infinitely many couplings.
Class. Quant. Grav. 20, 2355-2378
It is shown to all orders of perturbation theory, in
flat space or around a background of constant curvature,
that if the only term in the bare action containing two
Riemann tensors (and arbitrary numbers of derivatives)
is the Gauss—Bonnet invariant, then also the
renormalized action will have the same property. Thus,
if the classical propagator is quadratic in momenta,
also the renormalized propagator is quadratic in
momenta.
Damiano Anselmi (2005)
Infinite reduction of couplings in non-renormalizable quantum field theory.
JHEP 0508, 029
Damiano Anselmi and Milenko Halat (2006)
Dimensionally continued infinite reduction of couplings.
JHEP 0508, 029
These two papers describe a way in which a theory
containing infinitely many couplings can in reality
depend only on a finite number of parameters. The
techniques are quite different from the ones used in
recent work on asymptotic safety, but the effect seems
to be similar, with the independent parameters
corresponding to the coordinates in the UV critical
surface.
R. Foot, A. Kobakhidze, K.L. McDonald and R.R. Volkas (2008)
Renormalization-scale independence of the physical cosmological constant.
Phys. Lett. B664, 199-200
F. Bauer and L. Schrempp (2008)
Relaxing neutrino mass bounds by a running cosmological constant.
JCAP 0804, 006
I. Shapiro and J. Sola (2008)
Can the cosmological 'constant' run? - It may run
I. Shapiro and J. Sola (2009)
On the possible running of the cosmological
'constant'
Phys. Lett. B682, 105-113 (2009)
B.F.L. Ward (2009)
On the Running of the Cosmological Constant in Quantum General Relativity
Cosmic perturbations with running and
Lambda
Class. and Quantum Grav. 27, 105004 (2010)
B.F.L. Ward (2004)
Massive elementary particles and black holes.
JCAP 0402, 011.
Performs a resummation of perturbative series using the Yennie-Frautschi-Suura
method
and shows that point particles are not black holes as a
consequence of quantum effects.
B.F.L. Ward (2008)
Resummed quantum gravity.
Int. J. Mod. Phys. D17, 627-633
Presented at 33rd International Conference on High
Energy Physics (ICHEP 06), Moscow, Russia, 26 Jul - 2 Aug 2006.
Z. Bern (2002)
Perturbative Quantum Gravity and its Relation to Gauge Theory
Living Rev. Relativity, 5, lrr-2002-5, (2002). URL (cited on 15 May 2006):
http://www.livingreviews.org/lrr-2002-5
Z. Bern, J.J. Carrasco, D. Forde, H. Ita, H. Johansson (2007)
Unexpected Cancellations in Gravity Theories.
Phys. Rev. D77, 025010
Presents evidence that pure Einstein theory may have
unexpected cancellations.
Damiano Anselmi (2007)
Renormalization and causality violations in classical gravity coupled with quantum matter.
JHEP 0701:062
Damiano Anselmi, Milenko Halat (2007)
Renormalizable acausal theories of classical gravity coupled with interacting quantum fields
Class. Quant. Grav. 24, 1927-1954
These two papers deal with the renormalization of
quantum fields coupled to a classical metric.
Divergences are eliminated by redefinitions of the
metric, which becomes subject to RG flow.
A remark on quantum gravity
Ann. Phys. 323, 49-60 (2008)
By comparing the structure of the Dyson-Schwinger
equations for gravity to those of QED in 4 and 6
dimensions, it is suggested that gravity may be
renormalizable, in the sense that there may exist
infinitely many relations among all the amplitudes
needing renormalization, in such a way that only a
finite number of amplitudes remains undetermined.
Dario Benedetti (2008)
Fractal properties of quantum spacetime.
Phys. Rev. Lett. 102 111303 (2009)
It is shown that a scale dependent fractal dimension
appears in models of noncommutative geometry.
Leonardo Modesto (2008)
Fractal Structure of Loop Quantum Gravity.
It is shown that a scale dependent fractal dimension
appears in loop quantum gravity.
Petr Horava (2009a)
Quantum Gravity at a Lifshitz Point.
Phys. Rev. D79, 084008
A proposal for an UV complete theory of gravity, with
different number of derivatives in the spacelike and
timelike directions.
Petr Horava (2009b)
Spectral Dimension of the Universe in Quantum Gravity at a Lifshitz Point.
Phys. Rev. Lett. 102, 161301
Relates some results of the previous paper to those of
the CDT approach
I.L. Buchbinder, Sergei D. Odintsov and I. Shapiro
(1992)
Effective action in quantum gravity.
IOPP Publishing, Bristol.
A.M. Polyakov (1993)
A Few projects in string theory.
Les Houches Summer School 1992:0783-804 (QC178:H6:1992)
In this paper there is a brief discussion of the analogy
between gravity and the nonlinear sigma model,
suggesting the possibility that Newton’s constant may
run as demanded by its dimension at high energy.
E. Tomboulis (1996)
Exact relation between Einstein and quadratic quantum gravity.
Phys. Lett. B 389, 225.
Ali H. Chamseddine, Alain
Connes (1996)
The Spectral action principle.
Commun. Math. Phys. 186, 731-750
The spectral action is given by the trace of a function
of the Dirac operator. It uses the same mathematical
tools that are used to derive the gravitational beta
functions from the ERGE.
Ali H. Chamseddine, Alain
Connes (2010)
The Uncanny Precision of the
Spectral Action.
Commun. Math. Phys. 293, 867-897 (2010)
Detailed calculations of the spectral action for gravity
on the topology S1xS3.
Ali H. Chamseddine, Alain
Connes (2008)
The Space-time from the spectral point of view.
M. Reuter and C. Wetterich (1996a)
Quantum Liouville field theory as solution of a flow equation.
Nucl. Phys. B506, 483-520 (1997)
M. Reuter (1996b)
Weyl invariant quantization of Liouville field theory.
Presented at 3rd International Conference on
Renormalization Group (RG 96), Dubna, Russia, 26-31 Aug
1996.
Richard Woodard (2009)
How far are we from the quantum theory of
gravity?
This is a nice and up to
date review of the state of quantum gravity,
emphasizing technical issues and possible solutions.
Inflation is predicted to provide the first tests of
quantum gravity in the not too distant future.
Spontaneous
dimensional reduction in short-distance quantum gravity?
A. Codello (2010)
Polyakov effective action from functional renormalization group equation
Annals Phys. 325 1727-1738 (2010).
A derivation of the Polyakov action for 2d gravity
from the RG flow equation.
Benjamin
Koch and Israel Ramirez (2010)
Exact renormalization group with optimal scale and its application to cosmology
arXiv:1010.2799 [hep-th]Renormalization
group scale-setting in astrophysical systems
Phys. Lett. B703, 1-6 (2011)
A
different look at dark energy and time variation of the
fundamental constants
Wei Xue, Keshav Dasgupta and Robert Brandenberger (2011)
Cosmological
UV/IR divergences and de-Sitter spacetime
Phys.Rev. D83 (2011) 083520
arXiv:1103.0285
[hep-th]
G. Narain and R. Anishetty (2011)
Short distance freedom of quantum gravity
Phys.Lett. B711
(2012) 128-131
arXiv:1109.3981 [hep-th]
G. Narain and R. Anishetty (2012b)
Running couplings in quantum theory of gravity
coupled to gauge fields
JHEP 1310 (2013)
203
Yi Pang (2012)
One
loop divergences in 6D conformal gravity
Phys. Rev. D86, 084039 (2012)
I.Hamzaan Bridle, Juergen A. Dietz and Tim R. Morris (2013)
The
local potential approximation in the background field
formalism
JHEP 1403 (2014) 093
arXiv:1312.2846
[hep-th]
S. Jackson, R. Pourhassan and H. Verlinde (2013)
Geometric RG flow
Alessandro Codello, Giulio d'Odorico, Carlo Pagani (2013)
A
functional RG equation for the c-function
JHEP 1407 (2014) 040
This paper proposes a form for the c-function based on the functional RG, then gives some explicit checks in simple cases and a calculation of diagonal matrix elements of the Zamolodchikov metric.
Dario Benedetti (2014)
Critical behavior in
spherical and hyperbolic spacetime
J.Stat.Mech. 1501 (2015) P01002
A single scalar field theory with Z_2 symmetry is
studied on a spherical or hyperbolic background. The
presence of a fixed scale prevents the occurrence of a
true fixed point. On hyperbolic space a phase transition
exists and is governed by the Gaussian fixed point. In
the spherical case there is no phase transition: the
symmetry is always unbroken as one goes to sufficiently
low energy.
Richard Woodard (2014)
Perturbative quantum gravity comes of age
Int.J.Mod.Phys. D23 (2014) no.09, 1430020
Alessandro Codello, Giulio d'Odorico, Carlo Pagani (2013)
Functional
and local renormalization groups
Phys.Rev. D91 (2015) no.12, 125016
Carlo Pagani (2016)
A note on scaling arguments in the effective average action formalism
Astrid
Eichhorn, Lukas Janssen and Michael Scherer (2016)
Critical
O(N) models above four dimensions: Small-N solutions and
stability
Phys.Rev. D94 (2016) no.10, 104027
G. Narain (2016)
Exorcising ghosts in induced gravity
C. Wetterich (2016)
Gauge invariant flow equations
Daniel Litim, Edouard Marchais and Peter Mati (2017)
Fixed points and the spontaneous breaking of
scale invariance
G. Narain (2017)
Signs and stability in higher-derivative gravity
Christian Steinwachs and Alexander Yu. Kamenschik (2011)
One-loop
divergences for gravity non-minimally coupled to a multiplet
of scalar fields: calculation in the Jordan frame. I. The main
results.
Phys. Rev. D 84, 024026 (2011)
This paper contains a calculation of the one-loop divergences of a multiplet of scalars coupled to gravity. Contrary to earlier calculations, here the calculation is done entirely within the Jordan frame.
Michael S. Ruf and Christian Steinwachs (2017a)
One-loop
divergences for f(R)-gravity.
The one-loop logarithmic divergences of f(R)-gravity are calculated on an arbitrary background.
Michael S. Ruf and Christian Steinwachs (2017a)
Quantum
equivalence of f(R)-gravity and scalar-tensor theories.
Building on the results in the previous paper, it is shown that f(R)-gravity and the equivalent scalar-tensor theory have the same logarithmic one-loop divergences.
Benjamin Knorr (2018)
Lorentz
symmetry is relevant