#### Finite entanglement entropy in asymptotically safe quantum gravity

Journal of High Energy Physics
July 2018, 2018:39 | Cite as
Finite entanglement entropy in asymptotically safe quantum gravity
AuthorsAuthors and affiliations
Carlo PaganiMartin Reuter
Open Access
Regular Article - Theoretical Physics
First Online: 06 July 2018
Received: 17 April 2018
Revised: 28 May 2018
Accepted: 29 June 2018
38 Downloads
Abstract
Entanglement entropies calculated in the framework of quantum field theory on classical, flat or curved, spacetimes are known to show an intriguing area law in four dimensions, but they are also notorious for their quadratic ultraviolet divergences. In this paper we demonstrate that the analogous entanglement entropies when computed within the Asymptotic Safety approach to background independent quantum gravity are perfectly free from such divergences. We argue that the divergences are an artifact due to the over-idealization of a rigid, classical spacetime geometry which is insensitive to the quantum dynamics.
Keywords Models of Quantum Gravity Renormalization Group
ArXiv ePrint: 1804.02162
Download to read the full article text
Notes
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
References
[1]
S. Haroche and J.-M. Raimond, Exploring the Quantum, Oxford University Press (2006).Google Scholar
[2]
I. Bengtsson and K. Życzkowski, Geometry of Quantum States, Cambridge University Press (2006).Google Scholar
[3]
C.G. Callan Jr. and F. Wilczek, On geometric entropy, Phys. Lett. B 333 (1994) 55 [hep-th/9401072] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
[4]
D.N. Kabat and M.J. Strassler, A comment on entropy and area, Phys. Lett. B 329 (1994) 46 [hep-th/9401125] [INSPIRE].ADSCrossRefGoogle Scholar
[5]
S.N. Solodukhin, Entanglement entropy of black holes, Living Rev. Rel. 14 (2011) 8 [arXiv:1104.3712] [INSPIRE].CrossRefMATHGoogle Scholar
[6]
R.D. Sorkin, On The Entropy Of The Vacuum Outside A Horizon, in Tenth International Conference on General Relativity and Gravitation, Contributed Papers, vol. II, B. Bertotti, F. de Felice and A. Pascolini eds., Consiglio Nazionale Delle Ricerche (1983).Google Scholar
[7]
L. Bombelli, R.K. Koul, J. Lee and R.D. Sorkin, A Quantum Source of Entropy for Black Holes, Phys. Rev. D 34 (1986) 373 [INSPIRE].ADSMathSciNetMATHGoogle Scholar
[8]
M. Srednicki, Entropy and area, Phys. Rev. Lett. 71 (1993) 666 [hep-th/9303048] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
[9]
S.W. Hawking, Particle Creation by Black Holes, Commun. Math. Phys. 43 (1975) 199 [Erratum ibid. 46 (1976) 206] [INSPIRE].
[10]
J.D. Bekenstein, Black holes and entropy, Phys. Rev. D 7 (1973) 2333 [INSPIRE].ADSMathSciNetMATHGoogle Scholar
[11]
S.W. Hawking, Black Holes and Thermodynamics, Phys. Rev. D 13 (1976) 191 [INSPIRE].ADSGoogle Scholar
[12]
R.M. Wald, The thermodynamics of black holes, Living Rev. Rel. 4 (2001) 6 [gr-qc/9912119] [INSPIRE].
[13]
V.P. Frolov and I. Novikov, Dynamical origin of the entropy of a black hole, Phys. Rev. D 48 (1993) 4545 [gr-qc/9309001] [INSPIRE].
[14]
L. Susskind and J. Uglum, Black hole entropy in canonical quantum gravity and superstring theory, Phys. Rev. D 50 (1994) 2700 [hep-th/9401070] [INSPIRE].ADSMathSciNetGoogle Scholar
[15]
T. Jacobson, Black hole entropy and induced gravity, gr-qc/9404039 [INSPIRE].
[16]
S.N. Solodukhin, The Conical singularity and quantum corrections to entropy of black hole, Phys. Rev. D 51 (1995) 609 [hep-th/9407001] [INSPIRE].ADSMathSciNetGoogle Scholar
[17]
D.V. Fursaev, Black hole thermodynamics and renormalization, Mod. Phys. Lett. A 10 (1995) 649 [hep-th/9408066] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
[18]
J.-G. Demers, R. Lafrance and R.C. Myers, Black hole entropy without brick walls, Phys. Rev. D 52 (1995) 2245 [gr-qc/9503003] [INSPIRE].
[19]
D.N. Kabat, Black hole entropy and entropy of entanglement, Nucl. Phys. B 453 (1995) 281 [hep-th/9503016] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
[20]
F. Larsen and F. Wilczek, Renormalization of black hole entropy and of the gravitational coupling constant, Nucl. Phys. B 458 (1996) 249 [hep-th/9506066] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
[21]
T. Jacobson and A. Satz, Black hole entanglement entropy and the renormalization group, Phys. Rev. D 87 (2013) 084047 [arXiv:1212.6824] [INSPIRE].ADSGoogle Scholar
[22]
J.H. Cooperman and M.A. Luty, Renormalization of Entanglement Entropy and the Gravitational Effective Action, JHEP 12 (2014) 045 [arXiv:1302.1878] [INSPIRE].ADSCrossRefGoogle Scholar
[23]
A. Ashtekar, M. Reuter and C. Rovelli, From General Relativity to Quantum Gravity, arXiv:1408.4336 [INSPIRE].
[24]
S. Weinberg, Ultraviolet Divergences In Quantum Theories Of Gravitation, in General Relativity, an Einstein Centenary Survey, S.W. Hawking and W. Israel eds., Cambridge University Press (1980), pg. 790 [INSPIRE].
[25]
M. Reuter, Nonperturbative evolution equation for quantum gravity, Phys. Rev. D 57 (1998) 971 [hep-th/9605030] [INSPIRE].ADSMathSciNetGoogle Scholar
[26]
M. Niedermaier and M. Reuter, The Asymptotic Safety Scenario in Quantum Gravity, Living Rev. Rel. 9 (2006) 5 [INSPIRE].CrossRefMATHGoogle Scholar
[27]
R. Percacci, An Introduction To Covariant Quantum Gravity And Asymptotic Safety, World Scientific (2017).Google Scholar
[28]
M. Reuter and F. Saueressig, Quantum Gravity and the Functional Renormalization Group — The road towards Asymptotic Safety, Cambridge University Press, in press.Google Scholar
[29]
M. Reuter and F. Saueressig, Quantum Einstein Gravity, New J. Phys. 14 (2012) 055022 [arXiv:1202.2274] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
[30]
M. Reuter and F. Saueressig, Asymptotic Safety, Fractals and Cosmology, Lect. Notes Phys. 863 (2013) 185 [arXiv:1205.5431] [INSPIRE].ADSCrossRefMATHGoogle Scholar
[31]
M. Arzano and G. Calcagni, Finite entanglement entropy and spectral dimension in quantum gravity, Eur. Phys. J. C 77 (2017) 835 [arXiv:1704.01141] [INSPIRE].ADSCrossRefGoogle Scholar
[32]
T. Padmanabhan, Finite entanglement entropy from the zero-point-area of spacetime, Phys. Rev. D 82 (2010) 124025 [arXiv:1007.5066] [INSPIRE].ADSGoogle Scholar
[33]
J.S. Dowker, Quantum Field Theory on a Cone, J. Phys. A 10 (1977) 115 [INSPIRE].ADSMathSciNetGoogle Scholar
[34]
D.V. Fursaev, Spectral geometry and one loop divergences on manifolds with conical singularities, Phys. Lett. B 334 (1994) 53 [hep-th/9405143] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
[35]
C. Wetterich, Exact evolution equation for the effective potential, Phys. Lett. B 301 (1993) 90 [arXiv:1710.05815] [INSPIRE].ADSCrossRefGoogle Scholar
[36]
J.S. Schwinger, On gauge invariance and vacuum polarization, Phys. Rev. 82 (1951) 664 [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
[37]
W. Dittrich and M. Reuter, Effective Lagrangians In Quantum Electrodynamics, Lect. Notes Phys. 220 (1985) 1 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
[38]
C. Pagani and M. Reuter, Composite Operators in Asymptotic Safety, Phys. Rev. D 95 (2017) 066002 [arXiv:1611.06522] [INSPIRE].ADSGoogle Scholar
[39]
C. Pagani, Note on scaling arguments in the effective average action formalism, Phys. Rev. D 94 (2016) 045001 [arXiv:1603.07250] [INSPIRE].ADSMathSciNetGoogle Scholar
[40]
C. Pagani and H. Sonoda, Products of composite operators in the exact renormalization group formalism, PTEP 2018 (2018) 023B02 [arXiv:1707.09138] [INSPIRE].
[41]
M. Reuter and F. Saueressig, Renormalization group flow of quantum gravity in the Einstein-Hilbert truncation, Phys. Rev. D 65 (2002) 065016 [hep-th/0110054] [INSPIRE].ADSMathSciNetGoogle Scholar
[42]
E. Manrique and M. Reuter, Bare Action and Regularized Functional Integral of Asymptotically Safe Quantum Gravity, Phys. Rev. D 79 (2009) 025008 [arXiv:0811.3888] [INSPIRE].ADSGoogle Scholar
[43]
R. Percacci and G.P. Vacca, Search of scaling solutions in scalar-tensor gravity, Eur. Phys. J. C 75 (2015) 188 [arXiv:1501.00888] [INSPIRE].ADSCrossRefGoogle Scholar
[44]
N. Christiansen, D.F. Litim, J.M. Pawlowski and M. Reichert, Asymptotic safety of gravity with matter, Phys. Rev. D 97 (2018) 106012 [arXiv:1710.04669] [INSPIRE].ADSGoogle Scholar
[45]
D. Becker and M. Reuter, Towards a C-function in 4D quantum gravity, JHEP 03 (2015) 065 [arXiv:1412.0468] [INSPIRE].ADSCrossRefGoogle Scholar
[46]
M. Reuter and J.-M. Schwindt, A Minimal length from the cutoff modes in asymptotically safe quantum gravity, JHEP 01 (2006) 070 [hep-th/0511021] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
[47]
O. Lauscher and M. Reuter, Flow equation of quantum Einstein gravity in a higher derivative truncation, Phys. Rev. D 66 (2002) 025026 [hep-th/0205062] [INSPIRE].ADSMathSciNetGoogle Scholar
[48]
M. Reuter and F. Saueressig, A Class of nonlocal truncations in quantum Einstein gravity and its renormalization group behavior, Phys. Rev. D 66 (2002) 125001 [hep-th/0206145] [INSPIRE].ADSGoogle Scholar
[49]
A. Codello, R. Percacci and C. Rahmede, Ultraviolet properties of f (R)-gravity, Int. J. Mod. Phys. A 23 (2008) 143 [arXiv:0705.1769] [INSPIRE].ADSCrossRefMATHGoogle Scholar
[50]
D. Benedetti, P.F. Machado and F. Saueressig, Asymptotic safety in higher-derivative gravity, Mod. Phys. Lett. A 24 (2009) 2233 [arXiv:0901.2984] [INSPIRE].ADSCrossRefMATHGoogle Scholar
[51]
D. Benedetti, K. Groh, P.F. Machado and F. Saueressig, The Universal RG Machine, JHEP 06 (2011) 079 [arXiv:1012.3081] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
[52]
S. Rechenberger and F. Saueressig, The R 2 phase-diagram of QEG and its spectral dimension, Phys. Rev. D 86 (2012) 024018 [arXiv:1206.0657] [INSPIRE].ADSGoogle Scholar
[53]
N. Ohta and R. Percacci, Higher Derivative Gravity and Asymptotic Safety in Diverse Dimensions, Class. Quant. Grav. 31 (2014) 015024 [arXiv:1308.3398] [INSPIRE].ADSCrossRefMATHGoogle Scholar
[54]
D. Benedetti, On the number of relevant operators in asymptotically safe gravity, EPL 102 (2013) 20007 [arXiv:1301.4422] [INSPIRE].ADSCrossRefGoogle Scholar
[55]
K. Falls, D.F. Litim, K. Nikolakopoulos and C. Rahmede, Further evidence for asymptotic safety of quantum gravity, Phys. Rev. D 93 (2016) 104022 [arXiv:1410.4815] [INSPIRE].ADSMathSciNetGoogle Scholar
[56]
A. Eichhorn, The Renormalization Group flow of unimodular f(R) gravity, JHEP 04 (2015) 096 [arXiv:1501.05848] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
[57]
N. Ohta, R. Percacci and G.P. Vacca, Flow equation for f(R) gravity and some of its exact solutions, Phys. Rev. D 92 (2015) 061501 [arXiv:1507.00968] [INSPIRE].ADSGoogle Scholar
[58]
K. Falls, D.F. Litim, K. Nikolakopoulos and C. Rahmede, On de Sitter solutions in asymptotically safe f(R) theories, Class. Quant. Grav. 35 (2018) 135006 [arXiv:1607.04962] [INSPIRE].ADSCrossRefGoogle Scholar
[59]
K. Falls and N. Ohta, Renormalization Group Equation for f(R) gravity on hyperbolic spaces, Phys. Rev. D 94 (2016) 084005 [arXiv:1607.08460] [INSPIRE].ADSMathSciNetGoogle Scholar
[60]
H. Gies, B. Knorr, S. Lippoldt and F. Saueressig, Gravitational Two-Loop Counterterm Is Asymptotically Safe, Phys. Rev. Lett. 116 (2016) 211302 [arXiv:1601.01800] [INSPIRE].ADSCrossRefGoogle Scholar
[61]
M. Reuter and H. Weyer, Conformal sector of Quantum Einstein Gravity in the local potential approximation: Non-Gaussian fixed point and a phase of unbroken diffeomorphism invariance, Phys. Rev. D 80 (2009) 025001 [arXiv:0804.1475] [INSPIRE].ADSGoogle Scholar
[62]
D. Benedetti and F. Caravelli, The Local potential approximation in quantum gravity, JHEP 06 (2012) 017 [Erratum ibid. 10 (2012) 157] [arXiv:1204.3541] [INSPIRE].
[63]
M. Demmel, F. Saueressig and O. Zanusso, Fixed-Functionals of three-dimensional Quantum Einstein Gravity, JHEP 11 (2012) 131 [arXiv:1208.2038] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
[64]
J.A. Dietz and T.R. Morris, Asymptotic safety in the f(R) approximation, JHEP 01 (2013) 108 [arXiv:1211.0955] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
[65]
I.H. Bridle, J.A. Dietz and T.R. Morris, The local potential approximation in the background field formalism, JHEP 03 (2014) 093 [arXiv:1312.2846] [INSPIRE].ADSCrossRefGoogle Scholar
[66]
J.A. Dietz and T.R. Morris, Redundant operators in the exact renormalisation group and in the f(R) approximation to asymptotic safety, JHEP 07 (2013) 064 [arXiv:1306.1223] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
[67]
M. Demmel, F. Saueressig and O. Zanusso, RG flows of Quantum Einstein Gravity on maximally symmetric spaces, JHEP 06 (2014) 026 [arXiv:1401.5495] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
[68]
M. Demmel, F. Saueressig and O. Zanusso, RG flows of Quantum Einstein Gravity in the linear-geometric approximation, Annals Phys. 359 (2015) 141 [arXiv:1412.7207] [INSPIRE].MathSciNetCrossRefMATHGoogle Scholar
[69]
M. Demmel, F. Saueressig and O. Zanusso, A proper fixed functional for four-dimensional Quantum Einstein Gravity, JHEP 08 (2015) 113 [arXiv:1504.07656] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
[70]
N. Ohta, R. Percacci and G.P. Vacca, Renormalization Group Equation and scaling solutions for f(R) gravity in exponential parametrization, Eur. Phys. J. C 76 (2016) 46 [arXiv:1511.09393] [INSPIRE].ADSCrossRefGoogle Scholar
[71]
P. Labus, T.R. Morris and Z.H. Slade, Background independence in a background dependent renormalization group, Phys. Rev. D 94 (2016) 024007 [arXiv:1603.04772] [INSPIRE].ADSMathSciNetGoogle Scholar
[72]
J.A. Dietz, T.R. Morris and Z.H. Slade, Fixed point structure of the conformal factor field in quantum gravity, Phys. Rev. D 94 (2016) 124014 [arXiv:1605.07636] [INSPIRE].ADSMathSciNetGoogle Scholar
[73]
B. Knorr, Infinite order quantum-gravitational correlations, Class. Quant. Grav. 35 (2018) 115005 [arXiv:1710.07055] [INSPIRE].ADSCrossRefGoogle Scholar
[74]
N. Christiansen, K. Falls, J.M. Pawlowski and M. Reichert, Curvature dependence of quantum gravity, Phys. Rev. D 97 (2018) 046007 [arXiv:1711.09259] [INSPIRE].ADSGoogle Scholar
[75]
K. Falls, C.R. King, D.F. Litim, K. Nikolakopoulos and C. Rahmede, Asymptotic safety of quantum gravity beyond Ricci scalars, Phys. Rev. D 97 (2018) 086006 [arXiv:1801.00162] [INSPIRE].ADSGoogle Scholar
[76]
N. Alkofer and F. Saueressig, Asymptotically safe f(R)-gravity coupled to matter I: the polynomial case, arXiv:1802.00498 [INSPIRE].
[77]
E. Manrique and M. Reuter, Bimetric Truncations for Quantum Einstein Gravity and Asymptotic Safety, Annals Phys. 325 (2010) 785 [arXiv:0907.2617] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
[78]
E. Manrique, M. Reuter and F. Saueressig, Matter Induced Bimetric Actions for Gravity, Annals Phys. 326 (2011) 440 [arXiv:1003.5129] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
[79]
E. Manrique, M. Reuter and F. Saueressig, Bimetric Renormalization Group Flows in Quantum Einstein Gravity, Annals Phys. 326 (2011) 463 [arXiv:1006.0099] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
[80]
N. Christiansen, D.F. Litim, J.M. Pawlowski and A. Rodigast, Fixed points and infrared completion of quantum gravity, Phys. Lett. B 728 (2014) 114 [arXiv:1209.4038] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
[81]
A. Codello, G. D’Odorico and C. Pagani, Consistent closure of renormalization group flow equations in quantum gravity, Phys. Rev. D 89 (2014) 081701 [arXiv:1304.4777] [INSPIRE].ADSGoogle Scholar
[82]
N. Christiansen, B. Knorr, J.M. Pawlowski and A. Rodigast, Global Flows in Quantum Gravity, Phys. Rev. D 93 (2016) 044036 [arXiv:1403.1232] [INSPIRE].ADSMathSciNetGoogle Scholar
[83]
D. Becker and M. Reuter, En route to Background Independence: Broken split-symmetry and how to restore it with bi-metric average actions, Annals Phys. 350 (2014) 225 [arXiv:1404.4537] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
[84]
N. Christiansen, B. Knorr, J. Meibohm, J.M. Pawlowski and M. Reichert, Local Quantum Gravity, Phys. Rev. D 92 (2015) 121501 [arXiv:1506.07016] [INSPIRE].ADSGoogle Scholar
[85]
B. Knorr and S. Lippoldt, Correlation functions on a curved background, Phys. Rev. D 96 (2017) 065020 [arXiv:1707.01397] [INSPIRE].ADSGoogle Scholar
[86]
J.E. Daum and M. Reuter, Renormalization Group Flow of the Holst Action, Phys. Lett. B 710 (2012) 215 [arXiv:1012.4280] [INSPIRE].ADSCrossRefGoogle Scholar
[87]
J.E. Daum and M. Reuter, Einstein-Cartan gravity, Asymptotic Safety and the running Immirzi parameter, Annals Phys. 334 (2013) 351 [arXiv:1301.5135] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
[88]
C. Pagani and R. Percacci, Quantization and fixed points of non-integrable Weyl theory, Class. Quant. Grav. 31 (2014) 115005 [arXiv:1312.7767] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
[89]
C. Pagani and R. Percacci, Quantum gravity with torsion and non-metricity, Class. Quant. Grav. 32 (2015) 195019 [arXiv:1506.02882] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
[90]
M. Reuter and G.M. Schollmeyer, The metric on field space, functional renormalization and metric-torsion quantum gravity, Annals Phys. 367 (2016) 125 [arXiv:1509.05041] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
[91]
E. Manrique, S. Rechenberger and F. Saueressig, Asymptotically Safe Lorentzian Gravity, Phys. Rev. Lett. 106 (2011) 251302 [arXiv:1102.5012] [INSPIRE].ADSCrossRefGoogle Scholar
[92]
S. Rechenberger and F. Saueressig, A functional renormalization group equation for foliated spacetimes, JHEP 03 (2013) 010 [arXiv:1212.5114] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
[93]
J. Biemans, A. Platania and F. Saueressig, Quantum gravity on foliated spacetimes: Asymptotically safe and sound, Phys. Rev. D 95 (2017) 086013 [arXiv:1609.04813] [INSPIRE].ADSMATHGoogle Scholar
[94]
J. Biemans, A. Platania and F. Saueressig, Renormalization group fixed points of foliated gravity-matter systems, JHEP 05 (2017) 093 [arXiv:1702.06539] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
[95]
W.B. Houthoff, A. Kurov and F. Saueressig, Impact of topology in foliated Quantum Einstein Gravity, Eur. Phys. J. C 77 (2017) 491 [arXiv:1705.01848] [INSPIRE].ADSCrossRefGoogle Scholar
[96]
D. Dou and R. Percacci, The running gravitational couplings, Class. Quant. Grav. 15 (1998) 3449 [hep-th/9707239] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
[97]
R. Percacci and D. Perini, Constraints on matter from asymptotic safety, Phys. Rev. D 67 (2003) 081503 [hep-th/0207033] [INSPIRE].ADSGoogle Scholar
[98]
G. Narain and R. Percacci, Renormalization Group Flow in Scalar-Tensor Theories. I, Class. Quant. Grav. 27 (2010) 075001 [arXiv:0911.0386] [INSPIRE].
[99]
J.E. Daum, U. Harst and M. Reuter, Non-perturbative QEG Corrections to the Yang-Mills β-function, Gen. Relativ. Gravit. (2010) [arXiv:1005.1488] [INSPIRE].
[100]
S. Folkerts, D.F. Litim and J.M. Pawlowski, Asymptotic freedom of Yang-Mills theory with gravity, Phys. Lett. B 709 (2012) 234 [arXiv:1101.5552] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
[101]
U. Harst and M. Reuter, QED coupled to QEG, JHEP 05 (2011) 119 [arXiv:1101.6007] [INSPIRE].ADSCrossRefMATHGoogle Scholar
[102]
A. Eichhorn and H. Gies, Light fermions in quantum gravity, New J. Phys. 13 (2011) 125012 [arXiv:1104.5366] [INSPIRE].ADSCrossRefGoogle Scholar
[103]
A. Eichhorn, Quantum-gravity-induced matter self-interactions in the asymptotic-safety scenario, Phys. Rev. D 86 (2012) 105021 [arXiv:1204.0965] [INSPIRE].ADSGoogle Scholar
[104]
P. Donà and R. Percacci, Functional renormalization with fermions and tetrads, Phys. Rev. D 87 (2013) 045002 [arXiv:1209.3649] [INSPIRE].ADSGoogle Scholar
[105]
P. Donà, A. Eichhorn and R. Percacci, Matter matters in asymptotically safe quantum gravity, Phys. Rev. D 89 (2014) 084035 [arXiv:1311.2898] [INSPIRE].ADSGoogle Scholar
[106]
P. Labus, R. Percacci and G.P. Vacca, Asymptotic safety in O(N) scalar models coupled to gravity, Phys. Lett. B 753 (2016) 274 [arXiv:1505.05393] [INSPIRE].ADSCrossRefMATHGoogle Scholar
[107]
K.-y. Oda and M. Yamada, Non-minimal coupling in Higgs-Yukawa model with asymptotically safe gravity, Class. Quant. Grav. 33 (2016) 125011 [arXiv:1510.03734] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
[108]
J. Meibohm, J.M. Pawlowski and M. Reichert, Asymptotic safety of gravity-matter systems, Phys. Rev. D 93 (2016) 084035 [arXiv:1510.07018] [INSPIRE].ADSMathSciNetGoogle Scholar
[109]
P. Donà, A. Eichhorn, P. Labus and R. Percacci, Asymptotic safety in an interacting system of gravity and scalar matter, Phys. Rev. D 93 (2016) 044049 [Erratum ibid. D 93 (2016) 129904] [arXiv:1512.01589] [INSPIRE].
[110]
J. Meibohm and J.M. Pawlowski, Chiral fermions in asymptotically safe quantum gravity, Eur. Phys. J. C 76 (2016) 285 [arXiv:1601.04597] [INSPIRE].ADSCrossRefGoogle Scholar
[111]
A. Eichhorn, A. Held and J.M. Pawlowski, Quantum-gravity effects on a Higgs-Yukawa model, Phys. Rev. D 94 (2016) 104027 [arXiv:1604.02041] [INSPIRE].ADSMathSciNetGoogle Scholar
[112]
A. Eichhorn and S. Lippoldt, Quantum gravity and Standard-Model-like fermions, Phys. Lett. B 767 (2017) 142 [arXiv:1611.05878] [INSPIRE].ADSCrossRefGoogle Scholar
[113]
N. Christiansen and A. Eichhorn, An asymptotically safe solution to the U(1) triviality problem, Phys. Lett. B 770 (2017) 154 [arXiv:1702.07724] [INSPIRE].ADSCrossRefGoogle Scholar
[114]
A. Eichhorn and A. Held, Top mass from asymptotic safety, Phys. Lett. B 777 (2018) 217 [arXiv:1707.01107] [INSPIRE].ADSCrossRefGoogle Scholar
[115]
A. Eichhorn and F. Versteegen, Upper bound on the Abelian gauge coupling from asymptotic safety, JHEP 01 (2018) 030 [arXiv:1709.07252] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
[116]
D. Becker, C. Ripken and F. Saueressig, On avoiding Ostrogradski instabilities within Asymptotic Safety, JHEP 12 (2017) 121 [arXiv:1709.09098] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
[117]
F. Arici, D. Becker, C. Ripken, F. Saueressig and W.D. van Suijlekom, Reflection positivity in higher derivative scalar theories, arXiv:1712.04308 [INSPIRE].
[118]
O. Lauscher and M. Reuter, Fractal spacetime structure in asymptotically safe gravity, JHEP 10 (2005) 050 [hep-th/0508202] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
Copyright information
© The Author(s) 2018
Authors and Affiliations
Carlo Pagani1Email authorMartin Reuter11.Institute of PhysicsJohannes Gutenberg University MainzMainzGermany