Finite entanglement entropy in asymptotically safe quantum gravity

Journal of High Energy Physics, Jul 2018

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.

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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. Hawkin (...truncated)


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Carlo Pagani, Martin Reuter. Finite entanglement entropy in asymptotically safe quantum gravity, Journal of High Energy Physics, 2018, pp. 39, Volume 2018, Issue 7, DOI: 10.1007/JHEP07(2018)039