Abstract
We compute the four-derivative corrections to the geometry, extremality bound, and thermodynamic quantities of AdS-Reissner-Nordström black holes for general dimensions and horizon geometries. We confirm the universal relationship between the extremality shift at fixed charge and the shift of the microcanonical entropy, and discuss the consequences of this relation for the Weak Gravity Conjecture in AdS. The thermodynamic corrections are calculated using two different methods: first by explicitly solving the higher-derivative equations of motion and second, by evaluating the higher-derivative Euclidean on-shell action on the leading-order solution. In both cases we find agreement, up to the addition of a Casimir energy in odd dimensions. We derive the bounds on the four-derivative Wilson coefficients implied by the conjectured positivity of the leading corrections to the microcanonical entropy of thermodynamically stable black holes. These include the requirement that the coefficient of Riemann-squared is positive, meaning that the positivity of the entropy shift is related to the condition that c − a is positive in the dual CFT. We discuss implications for the deviation of η/s from its universal value and a potential lower bound.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
C. Vafa, The string landscape and the swampland, hep-th/0509212 [INSPIRE].
E. Palti, The swampland: introduction and review, Fortsch. Phys. 67 (2019) 1900037 [arXiv:1903.06239] [INSPIRE].
N. Arkani-Hamed, L. Motl, A. Nicolis and C. Vafa, The string landscape, black holes and gravity as the weakest force, JHEP 06 (2007) 060 [hep-th/0601001] [INSPIRE].
Y. Kats and P. Petrov, Effect of curvature squared corrections in AdS on the viscosity of the dual gauge theory, JHEP 01 (2009) 044 [arXiv:0712.0743] [INSPIRE].
C. Cheung and G.N. Remmen, Naturalness and the weak gravity conjecture, Phys. Rev. Lett. 113 (2014) 051601 [arXiv:1402.2287] [INSPIRE].
G. Shiu, P. Soler and W. Cottrell, Weak gravity conjecture and extremal black holes, Sci. China Phys. Mech. Astron. 62 (2019) 110412 [arXiv:1611.06270] [INSPIRE].
C. Cheung, J. Liu and G.N. Remmen, Proof of the weak gravity conjecture from black hole entropy, JHEP 10 (2018) 004 [arXiv:1801.08546] [INSPIRE].
S. Andriolo, D. Junghans, T. Noumi and G. Shiu, A tower weak gravity conjecture from infrared consistency, Fortsch. Phys. 66 (2018) 1800020 [arXiv:1802.04287] [INSPIRE].
Y. Hamada, T. Noumi and G. Shiu, Weak gravity conjecture from unitarity and causality, Phys. Rev. Lett. 123 (2019) 051601 [arXiv:1810.03637] [INSPIRE].
A.M. Charles, The weak gravity conjecture, RG flows, and supersymmetry, arXiv:1906.07734 [INSPIRE].
C.R.T. Jones and B. McPeak, The black hole weak gravity conjecture with multiple charges, JHEP 06 (2020) 140 [arXiv:1908.10452] [INSPIRE].
G. Goon and R. Penco, Universal relation between corrections to entropy and extremality, Phys. Rev. Lett. 124 (2020) 101103 [arXiv:1909.05254] [INSPIRE].
Y. Nakayama and Y. Nomura, Weak gravity conjecture in the AdS/CFT correspondence, Phys. Rev. D 92 (2015) 126006 [arXiv:1509.01647] [INSPIRE].
D. Harlow, Wormholes, emergent gauge fields, and the weak gravity conjecture, JHEP 01 (2016) 122 [arXiv:1510.07911] [INSPIRE].
M. Montero, G. Shiu and P. Soler, The weak gravity conjecture in three dimensions, JHEP 10 (2016) 159 [arXiv:1606.08438] [INSPIRE].
M. Montero, A holographic derivation of the weak gravity conjecture, JHEP 03 (2019) 157 [arXiv:1812.03978] [INSPIRE].
H.S. Reall and J.E. Santos, Higher derivative corrections to Kerr black hole thermodynamics, JHEP 04 (2019) 021 [arXiv:1901.11535] [INSPIRE].
R.C. Myers, M.F. Paulos and A. Sinha, Holographic hydrodynamics with a chemical potential, JHEP 06 (2009) 006 [arXiv:0903.2834] [INSPIRE].
Y. Kats, L. Motl and M. Padi, Higher-order corrections to mass-charge relation of extremal black holes, JHEP 12 (2007) 068 [hep-th/0606100] [INSPIRE].
S. Cremonini, J.T. Liu and P. Szepietowski, Higher derivative corrections to R-charged black holes: boundary counterterms and the mass-charge relation, JHEP 03 (2010) 042 [arXiv:0910.5159] [INSPIRE].
V. Balasubramanian and P. Kraus, A stress tensor for Anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [INSPIRE].
O. Loukas, D. Orlando, S. Reffert and D. Sarkar, An AdS/EFT correspondence at large charge, Nucl. Phys. B 934 (2018) 437 [arXiv:1804.04151] [INSPIRE].
R.M. Wald, Black hole entropy is the Noether charge, Phys. Rev. D 48 (1993) 3427 [gr-qc/9307038] [INSPIRE].
S.W. Hawking and W. Israel, General relativity. Cambridge University Press, Cambridge U.K. (19799.
J.W. York, Role of conformal three geometry in the dynamics of gravitation, Phys. Rev. Lett. 28 (1972) 1082 [INSPIRE].
G.W. Gibbons and S.W. Hawking, Action integrals and partition functions in quantum gravity, Phys. Rev. D 15 (1977) 2752 [INSPIRE].
S.W. Hawking and S.F. Ross, Duality between electric and magnetic black holes, Phys. Rev. D 52 (1995) 5865 [hep-th/9504019] [INSPIRE].
M. Henningson and K. Skenderis, The holographic Weyl anomaly, JHEP 07 (1998) 023 [hep-th/9806087] [INSPIRE].
R. Emparan, C.V. Johnson and R.C. Myers, Surface terms as counterterms in the AdS/CFT correspondence, Phys. Rev. D 60 (1999) 104001 [hep-th/9903238] [INSPIRE].
K. Skenderis, Lecture notes on holographic renormalization, Class. Quant. Grav. 19 (2002) 5849 [hep-th/0209067] [INSPIRE].
J.T. Liu and W.A. Sabra, Hamilton-Jacobi counterterms for Einstein-Gauss-Bonnet gravity, Class. Quant. Grav. 27 (2010) 175014 [arXiv:0807.1256] [INSPIRE].
C. Cheung, J. Liu and G.N. Remmen, Entropy bounds on effective field theory from rotating Dyonic black holes, Phys. Rev. D 100 (2019) 046003 [arXiv:1903.09156] [INSPIRE].
G.J. Loges, T. Noumi and G. Shiu, Thermodynamics of 4D dilatonic black holes and the weak gravity conjecture, Phys. Rev. D 102 (2020) 046010 [arXiv:1909.01352] [INSPIRE].
A. Chamblin, R. Emparan, C.V. Johnson and R.C. Myers, Charged AdS black holes and catastrophic holography, Phys. Rev. D 60 (1999) 064018 [hep-th/9902170] [INSPIRE].
A. Chamblin, R. Emparan, C.V. Johnson and R.C. Myers, Holography, thermodynamics and fluctuations of charged AdS black holes, Phys. Rev. D 60 (1999) 104026 [hep-th/9904197] [INSPIRE].
J.-y. Shen, R.-G. Cai, B. Wang and R.-K. Su, Thermodynamic geometry and critical behavior of black holes, Int. J. Mod. Phys. A 22 (2007) 11 [gr-qc/0512035] [INSPIRE].
C. Cheung and G.N. Remmen, Positivity of curvature-squared corrections in gravity, Phys. Rev. Lett. 118 (2017) 051601 [arXiv:1608.02942] [INSPIRE].
S. Nojiri and S.D. Odintsov, On the conformal anomaly from higher derivative gravity in AdS/CFT correspondence, Int. J. Mod. Phys. A 15 (2000) 413 [hep-th/9903033] [INSPIRE].
M. Blau, K.S. Narain and E. Gava, On subleading contributions to the AdS /CFT trace anomaly, JHEP 09 (1999) 018 [hep-th/9904179] [INSPIRE].
A. Buchel, R.C. Myers and A. Sinha, Beyond ηs = 1/4π, JHEP 03 (2009) 084 [arXiv:0812.2521] [INSPIRE].
D.M. Hofman and J. Maldacena, Conformal collider physics: Energy and charge correlations, JHEP 05 (2008) 012 [arXiv:0803.1467] [INSPIRE].
G. Policastro, D.T. Son and A.O. Starinets, The Shear viscosity of strongly coupled N = 4 supersymmetric Yang-Mills plasma, Phys. Rev. Lett. 87 (2001) 081601 [hep-th/0104066] [INSPIRE].
A. Buchel and J.T. Liu, Universality of the shear viscosity in supergravity, Phys. Rev. Lett. 93 (2004) 090602 [hep-th/0311175] [INSPIRE].
S. Cremonini, The shear viscosity to entropy ratio: a status report, Mod. Phys. Lett. B 25 (2011) 1867 [arXiv:1108.0677] [INSPIRE].
P. Kovtun and A. Ritz, Universal conductivity and central charges, Phys. Rev. D 78 (2008) 066009 [arXiv:0806.0110] [INSPIRE].
S. Cremonini and P. Szepietowski, Generating temperature flow for ηs with higher derivatives: from Lifshitz to AdS, JHEP 02 (2012) 038 [arXiv:1111.5623] [INSPIRE].
S. Cremonini, U. Gürsoy and P. Szepietowski, On the temperature dependence of the shear viscosity and holography, JHEP 08 (2012) 167 [arXiv:1206.3581] [INSPIRE].
S. Hellerman, D. Orlando, S. Reffert and M. Watanabe, On the CFT operator spectrum at large global charge, JHEP 12 (2015) 071 [arXiv:1505.01537] [INSPIRE].
S.S. Gubser, Breaking an abelian gauge symmetry near a black hole horizon, Phys. Rev. D 78 (2008) 065034 [arXiv:0801.2977] [INSPIRE].
S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Holographic superconductors, JHEP 12 (2008) 015 [arXiv:0810.1563] [INSPIRE].
S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Building a holographic superconductor, Phys. Rev. Lett. 101 (2008) 031601 [arXiv:0803.3295] [INSPIRE].
F. Denef and S.A. Hartnoll, Landscape of superconducting membranes, Phys. Rev. D 79 (2009) 126008 [arXiv:0901.1160] [INSPIRE].
S. Bhattacharyya, S. Minwalla and K. Papadodimas, Small hairy black holes in AdS5 × S5, JHEP 11 (2011) 035 [arXiv:1005.1287] [INSPIRE].
O.J.C. Dias, R. Monteiro, H.S. Reall and J.E. Santos, A scalar field condensation instability of rotating anti-de Sitter black holes, JHEP 11 (2010) 036 [arXiv:1007.3745] [INSPIRE].
T. Crisford, G.T. Horowitz and J.E. Santos, Testing the weak gravity — Cosmic censorship connection, Phys. Rev. D 97 (2018) 066005 [arXiv:1709.07880] [INSPIRE].
G.T. Horowitz and J.E. Santos, Further evidence for the weak gravity — Cosmic censorship connection, JHEP 06 (2019) 122 [arXiv:1901.11096] [INSPIRE].
G.T. Horowitz, J.E. Santos and B. Way, Evidence for an electrifying violation of cosmic censorship, Class. Quant. Grav. 33 (2016) 195007 [arXiv:1604.06465] [INSPIRE].
P.A. Cano, T. Ortín and P.F. Ramirez, On the extremality bound of stringy black holes, JHEP 02 (2020) 175 [arXiv:1909.08530] [INSPIRE].
P.A. Cano, S. Chimento, R. Linares, T. Ortín and P.F. Ramírez, α′ corrections of Reissner-Nordström black holes, JHEP 02 (2020) 031 [arXiv:1910.14324] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 1912.11161
Rights and permissions
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.
About this article
Cite this article
Cremonini, S., Jones, C.R., Liu, J.T. et al. Higher-derivative corrections to entropy and the weak gravity conjecture in Anti-de Sitter space. J. High Energ. Phys. 2020, 3 (2020). https://doi.org/10.1007/JHEP09(2020)003
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2020)003