Abstract
We embed general solutions to 4D Einstein-Maxwell theory into \( \mathcal{N}\ge 2 \) super-gravity and study quadratic fluctuations of the supergravity fields around the background. We compute one-loop quantum corrections for all fields and show that the c-anomaly vanishes for complete \( \mathcal{N}=2 \) multiplets. Logarithmic corrections to the entropy of Kerr-Newman black holes are therefore universal and independent of hole parameters.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S. Banerjee, R.K. Gupta and A. Sen, Logarithmic corrections to extremal black hole entropy from quantum entropy function, JHEP 03 (2011) 147 [arXiv:1005.3044] [INSPIRE].
S. Banerjee, R.K. Gupta, I. Mandal and A. Sen, Logarithmic corrections to N = 4 and N = 8 black hole entropy: a one loop test of quantum gravity, JHEP 11 (2011) 143 [arXiv:1106.0080] [INSPIRE].
A. Sen, Logarithmic corrections to N = 2 black hole entropy: an infrared window into the microstates, arXiv:1108.3842 [INSPIRE].
A. Sen, Microscopic and macroscopic entropy of extremal black holes in string theory, Gen. Rel. Grav. 46 (2014) 1711 [arXiv:1402.0109] [INSPIRE].
S. Hawking, Zeta function regularization of path integrals in curved space-time, Commun. Math. Phys. 55 (1977) 133.
N.D. Birrell and P.C.W. Davies, Quantum fields in curved space, Cambridge University Press, Cambridge U.K. (1982).
D.V. Vassilevich, Heat kernel expansion: user’s manual, Phys. Rept. 388 (2003) 279 [hep-th/0306138] [INSPIRE].
C. Keeler, F. Larsen and P. Lisbao, Logarithmic corrections to N ≥ 2 black hole entropy, Phys. Rev. D 90 (2014) 043011 [arXiv:1404.1379] [INSPIRE].
S. Bhattacharyya, B. Panda and A. Sen, Heat kernel expansion and extremal Kerr-Newmann black hole entropy in Einstein-Maxwell theory, JHEP 08 (2012) 084 [arXiv:1204.4061] [INSPIRE].
D.Z. Freedman and A. Van Proeyen, Supergravity, Cambridge University Press, Cambridge U.K. (2012).
S. Corley, Mass spectrum of N = 8 supergravity on AdS 2 × S 2, JHEP 09 (1999) 001 [hep-th/9906102] [INSPIRE].
B.S. DeWitt, Dynamical theory of groups and fields, North Carolina Univ., Chapel Hill U.S.A. (1963).
G. De Berredo-Peixoto, A note on the heat kernel method applied to fermions, Mod. Phys. Lett. A 16 (2001) 2463 [hep-th/0108223] [INSPIRE].
N.K. Nielsen, M.T. Grisaru, H. Romer and P. van Nieuwenhuizen, Approaches to the gravitational spin 3/2 axial anomaly, Nucl. Phys. B 140 (1978) 477 [INSPIRE].
R. Endo, Heat kernel for spin 3/2 Rarita-Schwinger field in general covariant gauge, Class. Quant. Grav. 12 (1995) 1157 [hep-th/9407019] [INSPIRE].
S.M. Christensen and M.J. Duff, Quantizing gravity with a cosmological constant, Nucl. Phys. B 170 (1980) 480 [INSPIRE].
S.M. Christensen and M.J. Duff, New gravitational index theorems and supertheorems, Nucl. Phys. B 154 (1979) 301 [INSPIRE].
S.M. Christensen and M.J. Duff, Axial and conformal anomalies for arbitrary spin in gravity and supergravity, Phys. Lett. B 76 (1978) 571 [INSPIRE].
G.W. Gibbons and M.J. Perry, Quantizing gravitational instantons, Nucl. Phys. B 146 (1978) 90 [INSPIRE].
G.W. Gibbons, S.W. Hawking and M.J. Perry, Path integrals and the indefiniteness of the gravitational action, Nucl. Phys. B 138 (1978) 141 [INSPIRE].
P.O. Mazur and E. Mottola, The gravitational measure, solution of the conformal factor problem and stability of the ground state of quantum gravity, Nucl. Phys. B 341 (1990) 187 [INSPIRE].
K. Schleich, Conformal rotation in perturbative gravity, Phys. Rev. D 36 (1987) 2342 [INSPIRE].
J.L. Cardy, Is there a c theorem in four-dimensions?, Phys. Lett. B 215 (1988) 749 [INSPIRE].
Z. Komargodski and A. Schwimmer, On renormalization group flows in four dimensions, JHEP 12 (2011) 099 [arXiv:1107.3987] [INSPIRE].
R.C. Myers and A. Sinha, Holographic c-theorems in arbitrary dimensions, JHEP 01 (2011) 125 [arXiv:1011.5819] [INSPIRE].
H. Elvang et al., On renormalization group flows and the a-theorem in 6D, JHEP 10 (2012) 011 [arXiv:1205.3994] [INSPIRE].
F. Larsen and P. Lisbao, Quantum corrections to supergravity on AdS 2 × S 2, Phys. Rev. D 91 (2015) 084056 [arXiv:1411.7423] [INSPIRE].
D. Anselmi, D.Z. Freedman, M.T. Grisaru and A.A. Johansen, Nonperturbative formulas for central functions of supersymmetric gauge theories, Nucl. Phys. B 526 (1998) 543 [hep-th/9708042] [INSPIRE].
D. Anselmi, J. Erlich, D.Z. Freedman and A.A. Johansen, Positivity constraints on anomalies in supersymmetric gauge theories, Phys. Rev. D 57 (1998) 7570 [hep-th/9711035] [INSPIRE].
R.C. Myers and A. Sinha, Seeing a c-theorem with holography, Phys. Rev. D 82 (2010) 046006 [arXiv:1006.1263] [INSPIRE].
V. Balasubramanian and P. Kraus, A stress tensor for Anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [INSPIRE].
M. Henningson and K. Skenderis, The holographic Weyl anomaly, JHEP 07 (1998) 023 [hep-th/9806087] [INSPIRE].
D.Z. Freedman, S.S. Gubser, K. Pilch and N.P. Warner, Renormalization group flows from holography supersymmetry and a c theorem, Adv. Theor. Math. Phys. 3 (1999) 363 [hep-th/9904017] [INSPIRE].
S.S. Gubser, Einstein manifolds and conformal field theories, Phys. Rev. D 59 (1999) 025006 [hep-th/9807164] [INSPIRE].
S. Benvenuti and A. Hanany, New results on superconformal quivers, JHEP 04 (2006) 032 [hep-th/0411262] [INSPIRE].
A. Sen, Logarithmic corrections to rotating extremal black hole entropy in four and five dimensions, Gen. Rel. Grav. 44 (2012) 1947 [arXiv:1109.3706] [INSPIRE].
A. Sen, Logarithmic corrections to Schwarzschild and other non-extremal black hole entropy in different dimensions, JHEP 04 (2013) 156 [arXiv:1205.0971] [INSPIRE].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1505.01156
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Charles, A.M., Larsen, F. Universal corrections to non-extremal black hole entropy in \( \mathcal{N}\ge 2 \) supergravity. J. High Energ. Phys. 2015, 200 (2015). https://doi.org/10.1007/JHEP06(2015)200
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2015)200