Abstract
In this paper we discuss the supersymmetric localization of the 4D \( \mathcal{N} \) = 2 offshell gauged supergravity on the background of the AdS4 neutral topological black hole, which is the gravity dual of the ABJM theory defined on the boundary \( {\mathrm{S}}^1\times {\mathrm{\mathbb{H}}}^2 \). We compute the large-N expansion of the supergravity partition function. The result gives the black hole entropy with the logarithmic correction, which matches the previous result of the entanglement entropy of the ABJM theory up to some stringy effects. Our result is consistent with the previous on-shell one-loop computation of the logarithmic correction to black hole entropy. It provides an explicit example of the identification of the entanglement entropy of the boundary conformal field theory with the bulk black hole entropy beyond the leading order given by the classical Bekenstein-Hawking formula, which consequently tests the AdS/CFT correspondence at the subleading order.
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References
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
T. Nishioka and I. Yaakov, Supersymmetric Renyi Entropy, JHEP 10 (2013) 155 [arXiv:1306.2958] [INSPIRE].
V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun. Math. Phys. 313 (2012) 71 [arXiv:0712.2824] [INSPIRE].
N. Hama, K. Hosomichi and S. Lee, SUSY Gauge Theories on Squashed Three-Spheres, JHEP 05 (2011) 014 [arXiv:1102.4716] [INSPIRE].
Y. Imamura and D. Yokoyama, N = 2 supersymmetric theories on squashed three-sphere, Phys. Rev. D 85 (2012) 025015 [arXiv:1109.4734] [INSPIRE].
L.F. Alday, D. Martelli, P. Richmond and J. Sparks, Localization on Three-Manifolds, JHEP 10 (2013) 095 [arXiv:1307.6848] [INSPIRE].
J. Nian, Localization of Supersymmetric Chern-Simons-Matter Theory on a Squashed S 3 with SU(2) × U(1) Isometry, JHEP 07 (2014) 126 [arXiv:1309.3266] [INSPIRE].
A. Tanaka, Localization on round sphere revisited, JHEP 11 (2013) 103 [arXiv:1309.4992] [INSPIRE].
M. Mariño and P. Putrov, ABJM theory as a Fermi gas, J. Stat. Mech. 1203 (2012) P03001 [arXiv:1110.4066] [INSPIRE].
Y. Hatsuda, ABJM on ellipsoid and topological strings, JHEP 07 (2016) 026 [arXiv:1601.02728] [INSPIRE].
X. Huang, S.-J. Rey and Y. Zhou, Three-dimensional SCFT on conic space as hologram of charged topological black hole, JHEP 03 (2014) 127 [arXiv:1401.5421] [INSPIRE].
T. Nishioka, The Gravity Dual of Supersymmetric Renyi Entropy, JHEP 07 (2014) 061 [arXiv:1401.6764] [INSPIRE].
X. Huang and Y. Zhou, \( \mathcal{N} \) = 4 super-Yang-Mills on conic space as hologram of STU topological black hole, JHEP 02 (2015) 068 [arXiv:1408.3393] [INSPIRE].
M. Crossley, E. Dyer and J. Sonner, Super-Rényi entropy & Wilson loops for \( \mathcal{N} \) = 4 SYM and their gravity duals, JHEP 12 (2014) 001 [arXiv:1409.0542] [INSPIRE].
L.F. Alday, P. Richmond and J. Sparks, The holographic supersymmetric Renyi entropy in five dimensions, JHEP 02 (2015) 102 [arXiv:1410.0899] [INSPIRE].
N. Hama, T. Nishioka and T. Ugajin, Supersymmetric Rényi entropy in five dimensions, JHEP 12 (2014) 048 [arXiv:1410.2206] [INSPIRE].
A. Giveon and D. Kutasov, Supersymmetric Renyi entropy in CFT 2 and AdS 3, JHEP 01 (2016) 042 [arXiv:1510.08872] [INSPIRE].
H. Mori, Supersymmetric Rényi entropy in two dimensions, JHEP 03 (2016) 058 [arXiv:1512.02829] [INSPIRE].
J. Nian and Y. Zhou, Rényi entropy of a free (2, 0) tensor multiplet and its supersymmetric counterpart, Phys. Rev. D 93 (2016) 125010 [arXiv:1511.00313] [INSPIRE].
Y. Zhou, Supersymmetric Rényi entropy and Weyl anomalies in six-dimensional (2, 0) theories, JHEP 06 (2016) 064 [arXiv:1512.03008] [INSPIRE].
A. Dabholkar, J. Gomes and S. Murthy, Quantum black holes, localization and the topological string, JHEP 06 (2011) 019 [arXiv:1012.0265] [INSPIRE].
A. Dabholkar, J. Gomes and S. Murthy, Localization & Exact Holography, JHEP 04 (2013) 062 [arXiv:1111.1161] [INSPIRE].
A. Dabholkar, N. Drukker and J. Gomes, Localization in supergravity and quantum AdS 4 /CF T 3 holography, JHEP 10 (2014) 90 [arXiv:1406.0505] [INSPIRE].
O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [INSPIRE].
S.W. Hawking, Gravitational radiation from colliding black holes, Phys. Rev. Lett. 26 (1971) 1344 [INSPIRE].
J.D. Bekenstein, Black holes and the second law, Lett. Nuovo Cim. 4 (1972) 737 [INSPIRE].
J.D. Bekenstein, Black holes and entropy, Phys. Rev. D 7 (1973) 2333 [INSPIRE].
S. Bhattacharyya, A. Grassi, M. Mariño and A. Sen, A One-Loop Test of Quantum Supergravity, Class. Quant. Grav. 31 (2014) 015012 [arXiv:1210.6057] [INSPIRE].
F. van de Bult, Hyperbolic hypergeometric functions, Ph.D. Thesis, University of Amsterdam (2007).
A. Kapustin, B. Willett and I. Yaakov, Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter, JHEP 03 (2010) 089 [arXiv:0909.4559] [INSPIRE].
C.P. Herzog, I.R. Klebanov, S.S. Pufu and T. Tesileanu, Multi-Matrix Models and Tri-Sasaki Einstein Spaces, Phys. Rev. D 83 (2011) 046001 [arXiv:1011.5487] [INSPIRE].
D. Martelli and J. Sparks, The large-N limit of quiver matrix models and Sasaki-Einstein manifolds, Phys. Rev. D 84 (2011) 046008 [arXiv:1102.5289] [INSPIRE].
D.R. Brill, J. Louko and P. Peldan, Thermodynamics of (3 + 1)-dimensional black holes with toroidal or higher genus horizons, Phys. Rev. D 56 (1997) 3600 [gr-qc/9705012] [INSPIRE].
D.Z. Freedman and A.K. Das, Gauge Internal Symmetry in Extended Supergravity, Nucl. Phys. B 120 (1977) 221 [INSPIRE].
N. Alonso-Alberca, P. Meessen and T. Ortín, Supersymmetry of topological Kerr-Newman-Taub-NUT-AdS space-times, Class. Quant. Grav. 17 (2000) 2783 [hep-th/0003071] [INSPIRE].
B. de Wit, P.G. Lauwers and A. Van Proeyen, Lagrangians of N = 2 Supergravity-Matter Systems, Nucl. Phys. B 255 (1985) 569 [INSPIRE].
D.E. Diaz and H. Dorn, Partition functions and double-trace deformations in AdS/CFT, JHEP 05 (2007) 046 [hep-th/0702163] [INSPIRE].
J. Maldacena and G.L. Pimentel, Entanglement entropy in de Sitter space, JHEP 02 (2013) 038 [arXiv:1210.7244] [INSPIRE].
E. Witten, Analytic Continuation Of Chern-Simons Theory, AMS/IP Stud. Adv. Math. 50 (2011) 347 [arXiv:1001.2933] [INSPIRE].
A. Lewkowycz and J. Maldacena, Generalized gravitational entropy, JHEP 08 (2013) 090 [arXiv:1304.4926] [INSPIRE].
J.R. David, E. Gava, R.K. Gupta and K. Narain, Localization on AdS 2 × S 1, JHEP 03 (2017) 050 [arXiv:1609.07443] [INSPIRE].
B. Assel, D. Martelli, S. Murthy and D. Yokoyama, Localization of supersymmetric field theories on non-compact hyperbolic three-manifolds, JHEP 03 (2017) 095 [arXiv:1609.08071] [INSPIRE].
A. Cabo-Bizet, V.I. Giraldo-Rivera and L.A. Pando Zayas, Microstate Counting of AdS 4 Hyperbolic Black Hole Entropy via the Topologically Twisted Index, arXiv:1701.07893 [INSPIRE].
F. Benini, K. Hristov and A. Zaffaroni, Black hole microstates in AdS 4 from supersymmetric localization, JHEP 05 (2016) 054 [arXiv:1511.04085] [INSPIRE].
J. Gomes, Quantum entropy and exact 4d/5d connection, JHEP 01 (2015) 109 [arXiv:1305.2849] [INSPIRE].
S. Murthy and V. Reys, Functional determinants, index theorems and exact quantum black hole entropy, JHEP 12 (2015) 028 [arXiv:1504.01400] [INSPIRE].
R.K. Gupta, Y. Ito and I. Jeon, Supersymmetric Localization for BPS Black Hole Entropy: 1-loop Partition Function from Vector Multiplets, JHEP 11 (2015) 197 [arXiv:1504.01700] [INSPIRE].
J. Gomes, Exact Holography and Black Hole Entropy in \( \mathcal{N} \) = 8 and \( \mathcal{N} \) = 4 String Theory, JHEP 07 (2017) 022 [arXiv:1511.07061] [INSPIRE].
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, Gen. Rel. Grav. 44 (2012) 1207 [arXiv:1108.3842] [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].
G. Festuccia and N. Seiberg, Rigid Supersymmetric Theories in Curved Superspace, JHEP 06 (2011) 114 [arXiv:1105.0689] [INSPIRE].
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Nian, J., Zhang, X. Entanglement entropy of ABJM theory and entropy of topological black hole. J. High Energ. Phys. 2017, 96 (2017). https://doi.org/10.1007/JHEP07(2017)096
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DOI: https://doi.org/10.1007/JHEP07(2017)096