Abstract
Recent derivations of Cardy-like formulae in higher dimensional field theories have opened up a way of computing, via AdS/CFT, universal contributions to black hole entropy from gravitational Chern-Simons terms. Based on the manifestly covariant formulation of the differential Noether charge for Chern-Simons terms proposed in [1], we compute the entropy and asymptotic charges for the rotating charged AdS black holes in higher dimensions at leading order of the fluid/gravity derivative expansion in the EinsteinMaxwell-Chern-Simons system. This gives a result that exactly matches the field theory predictions from Cardy-like formulae.
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T. Azeyanagi, R. Loganayagam, G.S. Ng and M.J. Rodriguez, Covariant Noether charge for higher dimensional Chern-Simons terms, JHEP 05 (2015) 041 [arXiv:1407.6364] [INSPIRE].
A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett. B 379 (1996) 99 [hep-th/9601029] [INSPIRE].
C.G. Callan and J.M. Maldacena, D-brane approach to black hole quantum mechanics, Nucl. Phys. B 472 (1996) 591 [hep-th/9602043] [INSPIRE].
M. Cvetič and A.A. Tseytlin, Nonextreme black holes from nonextreme intersecting M-branes, Nucl. Phys. B 478 (1996) 181 [hep-th/9606033] [INSPIRE].
G.T. Horowitz, J.M. Maldacena and A. Strominger, Nonextremal black hole microstates and U duality, Phys. Lett. B 383 (1996) 151 [hep-th/9603109] [INSPIRE].
J.M. Maldacena and A. Strominger, Statistical entropy of four-dimensional extremal black holes, Phys. Rev. Lett. 77 (1996) 428 [hep-th/9603060] [INSPIRE].
C.V. Johnson, R.R. Khuri and R.C. Myers, Entropy of 4D extremal black holes, Phys. Lett. B 378 (1996) 78 [hep-th/9603061] [INSPIRE].
J.M. Maldacena, A. Strominger and E. Witten, Black hole entropy in M-theory, JHEP 12 (1997) 002 [hep-th/9711053] [INSPIRE].
J.L. Cardy, Operator content of two-dimensional conformally invariant theories, Nucl. Phys. B 270 (1986) 186 [INSPIRE].
A. Strominger, Black hole entropy from near horizon microstates, JHEP 02 (1998) 009 [hep-th/9712251] [INSPIRE].
K. Landsteiner, E. Megias and F. Pena-Benitez, Gravitational anomaly and transport, Phys. Rev. Lett. 107 (2011) 021601 [arXiv:1103.5006] [INSPIRE].
K. Landsteiner, E. Megias, L. Melgar and F. Pena-Benitez, Holographic gravitational anomaly and chiral vortical effect, JHEP 09 (2011) 121 [arXiv:1107.0368] [INSPIRE].
R. Loganayagam and P. Surowka, Anomaly/transport in an ideal Weyl gas, JHEP 04 (2012) 097 [arXiv:1201.2812] [INSPIRE].
R. Loganayagam, Anomalies and the helicity of the thermal state, JHEP 11 (2013) 205 [arXiv:1211.3850] [INSPIRE].
K. Jensen, R. Loganayagam and A. Yarom, Thermodynamics, gravitational anomalies and cones, JHEP 02 (2013) 088 [arXiv:1207.5824] [INSPIRE].
K. Jensen, R. Loganayagam and A. Yarom, Anomaly inflow and thermal equilibrium, JHEP 05 (2014) 134 [arXiv:1310.7024] [INSPIRE].
K. Jensen, R. Loganayagam and A. Yarom, Chern-Simons terms from thermal circles and anomalies, JHEP 05 (2014) 110 [arXiv:1311.2935] [INSPIRE].
V.P. Spiridonov and G.S. Vartanov, Elliptic hypergeometric integrals and ’t Hooft anomaly matching conditions, JHEP 06 (2012) 016 [arXiv:1203.5677] [INSPIRE].
B. Assel, D. Cassani and D. Martelli, Localization on Hopf surfaces, JHEP 08 (2014) 123 [arXiv:1405.5144] [INSPIRE].
M. Buican, T. Nishinaka and C. Papageorgakis, Constraints on chiral operators in N = 2 SCFTs, JHEP 12 (2014) 095 [arXiv:1407.2835] [INSPIRE].
A.A. Ardehali, J.T. Liu and P. Szepietowski, c − a from the N = 1 superconformal index, JHEP 12 (2014) 145 [arXiv:1407.6024] [INSPIRE].
L. Di Pietro and Z. Komargodski, Cardy formulae for SUSY theories in d = 4 and d = 6, JHEP 12 (2014) 031 [arXiv:1407.6061] [INSPIRE].
A.A. Ardehali, J.T. Liu and P. Szepietowski, Central charges from the N = 1 superconformal index, Phys. Rev. Lett. 114 (2015) 091603 [arXiv:1411.5028] [INSPIRE].
J. Lorenzen and D. Martelli, Comments on the Casimir energy in supersymmetric field theories, JHEP 07 (2015) 001 [arXiv:1412.7463] [INSPIRE].
A.A. Ardehali, J.T. Liu and P. Szepietowski, High-temperature expansion of supersymmetric partition functions, JHEP 07 (2015) 113 [arXiv:1502.07737] [INSPIRE].
B. Assel, D. Cassani, L. Di Pietro, Z. Komargodski, J. Lorenzen and D. Martelli, The Casimir energy in curved space and its supersymmetric counterpart, JHEP 07 (2015) 043 [arXiv:1503.05537] [INSPIRE].
T. Azeyanagi, R. Loganayagam, G.S. Ng and M.J. Rodriguez, Holographic thermal helicity, JHEP 08 (2014) 040 [arXiv:1311.2940] [INSPIRE].
J. Lee and R.M. Wald, Local symmetries and constraints, J. Math. Phys. 31 (1990) 725 [INSPIRE].
R.M. Wald, Black hole entropy is the Noether charge, Phys. Rev. D 48 (1993) 3427 [gr-qc/9307038] [INSPIRE].
V. Iyer and R.M. Wald, Some properties of Noether charge and a proposal for dynamical black hole entropy, Phys. Rev. D 50 (1994) 846 [gr-qc/9403028] [INSPIRE].
Y. Tachikawa, Black hole entropy in the presence of Chern-Simons terms, Class. Quant. Grav. 24 (2007) 737 [hep-th/0611141] [INSPIRE].
L. Bonora, M. Cvitan, P. Dominis Prester, S. Pallua and I. Smolic, Gravitational Chern-Simons Lagrangians and black hole entropy, JHEP 07 (2011) 085 [arXiv:1104.2523] [INSPIRE].
S. Bhattacharyya et al., Local fluid dynamical entropy from gravity, JHEP 06 (2008) 055 [arXiv:0803.2526] [INSPIRE].
T. Jacobson, G. Kang and R.C. Myers, On black hole entropy, Phys. Rev. D 49 (1994) 6587 [gr-qc/9312023] [INSPIRE].
F.M. Haehl, R. Loganayagam and M. Rangamani, Adiabatic hydrodynamics: the eightfold way to dissipation, JHEP 05 (2015) 060 [arXiv:1502.00636] [INSPIRE].
R. Loganayagam, Anomaly induced transport in arbitrary dimensions, arXiv:1106.0277 [INSPIRE].
N. Banerjee, S. Dutta, S. Jain, R. Loganayagam and T. Sharma, Constraints on anomalous fluid in arbitrary dimensions, JHEP 03 (2013) 048 [arXiv:1206.6499] [INSPIRE].
U. Gürsoy and A. Jansen, (Non)renormalization of anomalous conductivities and holography, JHEP 10 (2014) 92 [arXiv:1407.3282] [INSPIRE].
U. Gürsoy and J. Tarrio, Horizon universality and anomalous conductivities, arXiv:1410.1306 [INSPIRE].
S. Chapman, Y. Neiman and Y. Oz, Fluid/gravity correspondence, local Wald entropy current and gravitational anomaly, JHEP 07 (2012) 128 [arXiv:1202.2469] [INSPIRE].
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
A. Lewkowycz and J. Maldacena, Generalized gravitational entropy, JHEP 08 (2013) 090 [arXiv:1304.4926] [INSPIRE].
X. Dong, Holographic entanglement entropy for general higher derivative gravity, JHEP 01 (2014) 044 [arXiv:1310.5713] [INSPIRE].
J. Camps, Generalized entropy and higher derivative gravity, JHEP 03 (2014) 070 [arXiv:1310.6659] [INSPIRE].
A. Bhattacharyya, A. Kaviraj and A. Sinha, Entanglement entropy in higher derivative holography, JHEP 08 (2013) 012 [arXiv:1305.6694] [INSPIRE].
A. Bhattacharyya, M. Sharma and A. Sinha, On generalized gravitational entropy, squashed cones and holography, JHEP 01 (2014) 021 [arXiv:1308.5748] [INSPIRE].
A. Bhattacharyya and M. Sharma, On entanglement entropy functionals in higher derivative gravity theories, JHEP 10 (2014) 130 [arXiv:1405.3511] [INSPIRE].
N. Lashkari, M.B. McDermott and M. Van Raamsdonk, Gravitational dynamics from entanglement ‘thermodynamics’, JHEP 04 (2014) 195 [arXiv:1308.3716] [INSPIRE].
T. Faulkner, M. Guica, T. Hartman, R.C. Myers and M. Van Raamsdonk, Gravitation from entanglement in holographic CFTs, JHEP 03 (2014) 051 [arXiv:1312.7856] [INSPIRE].
S. Banerjee, A. Bhattacharyya, A. Kaviraj, K. Sen and A. Sinha, Constraining gravity using entanglement in AdS/CFT, JHEP 05 (2014) 029 [arXiv:1401.5089] [INSPIRE].
T. Faulkner, Bulk emergence and the RG flow of entanglement entropy, JHEP 05 (2015) 033 [arXiv:1412.5648] [INSPIRE].
A. Castro, S. Detournay, N. Iqbal and E. Perlmutter, Holographic entanglement entropy and gravitational anomalies, JHEP 07 (2014) 114 [arXiv:1405.2792] [INSPIRE].
T. Azeyanagi, R. Loganayagam and G.S. Ng, Holographic entanglement for Chern-Simons terms, arXiv:1507.02298 [INSPIRE].
S. Kobayashi and K. Nomizu, Foundations of differential geometry, volume 2, Wiley-Interscience, U.S.A. (1996).
M. Nakahara, Geometry, topology and physics, second edition, Graduate Student Series in Physics, CRC Press, U.S.A. (2003).
P. Kraus, Lectures on black holes and the AdS 3 /CFT 2 correspondence, Lect. Notes Phys. 755 (2008) 193 [hep-th/0609074] [INSPIRE].
G. Compere, K. Murata and T. Nishioka, Central charges in extreme black hole/CFT correspondence, JHEP 05 (2009) 077 [arXiv:0902.1001] [INSPIRE].
B. Sahoo and H.-U. Yee, Electrified plasma in AdS/CFT correspondence, JHEP 11 (2010) 095 [arXiv:1004.3541] [INSPIRE].
D.E. Kharzeev and H.-U. Yee, Anomalies and time reversal invariance in relativistic hydrodynamics: the second order and higher dimensional formulations, Phys. Rev. D 84 (2011) 045025 [arXiv:1105.6360] [INSPIRE].
R. Baier, P. Romatschke, D.T. Son, A.O. Starinets and M.A. Stephanov, Relativistic viscous hydrodynamics, conformal invariance and holography, JHEP 04 (2008) 100 [arXiv:0712.2451] [INSPIRE].
R. Loganayagam, Entropy current in conformal hydrodynamics, JHEP 05 (2008) 087 [arXiv:0801.3701] [INSPIRE].
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Azeyanagi, T., Loganayagam, R. & Ng, G.S. Anomalies, Chern-Simons terms and black hole entropy. J. High Energ. Phys. 2015, 121 (2015). https://doi.org/10.1007/JHEP09(2015)121
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DOI: https://doi.org/10.1007/JHEP09(2015)121