Microstate counting of \(\mathrm{AdS}_{4}\) hyperbolic black hole entropy via the topologically twisted index. (English) Zbl 1381.83055
Summary: We compute the topologically twisted index for general \( \mathcal{N}=2 \) supersymmetric field theories on \( {{\mathbb{H}}}_2\times {S}^1 \). We also discuss asymptotically \(\mathrm{AdS}_{4}\) magnetically charged black holes with hyperbolic horizon, in four-dimensional \( \mathcal{N}=2 \) gauged supergravity. With certain assumptions, put forward by F. Benini, K. Hristov and A. Zaffaroni, “Black hole microstates in \(\mathrm{AdS}_{4}\) from supersymmetric localization”, [J. High Energy Phys. 2016, No. 5, Paper No. 054, 57 p. (2016; arXiv:1511.04085)], we find precise agreement between the black hole entropy and the topologically twisted index, for ABJM theories.
MSC:
| 83C57 | Black holes |
| 94A17 | Measures of information, entropy |
| 83E30 | String and superstring theories in gravitational theory |
| 58J28 | Eta-invariants, Chern-Simons invariants |
| 81T60 | Supersymmetric field theories in quantum mechanics |
Keywords:
AdS-CFT correspondence; black holes in string theory; Chern-Simons theories; supersymmetric gauge theoryReferences:
| [1] | A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett.B 379 (1996) 99 [hep-th/9601029] [INSPIRE]. · Zbl 1376.83026 · doi:10.1016/0370-2693(96)00345-0 |
| [2] | F. Benini, K. Hristov and A. Zaffaroni, Black hole microstates in AdS4from supersymmetric localization, JHEP05 (2016) 054 [arXiv:1511.04085] [INSPIRE]. · Zbl 1388.83388 · doi:10.1007/JHEP05(2016)054 |
| [3] | F. Benini and A. Zaffaroni, A topologically twisted index for three-dimensional supersymmetric theories, JHEP07 (2015) 127 [arXiv:1504.03698] [INSPIRE]. · Zbl 1388.81400 · doi:10.1007/JHEP07(2015)127 |
| [4] | S.M. Hosseini and A. Zaffaroni, Large-N matrix models for \[3dN=2 \mathcal{N}=2\] theories: twisted index, free energy and black holes, JHEP08 (2016) 064 [arXiv:1604.03122] [INSPIRE]. · Zbl 1390.83345 · doi:10.1007/JHEP08(2016)064 |
| [5] | S.M. Hosseini and N. Mekareeya, Large-N topologically twisted index: necklace quivers, dualities and Sasaki-Einstein spaces, JHEP08 (2016) 089 [arXiv:1604.03397] [INSPIRE]. · Zbl 1390.81600 · doi:10.1007/JHEP08(2016)089 |
| [6] | C. Closset and H. Kim, Comments on twisted indices in 3d supersymmetric gauge theories, JHEP08 (2016) 059 [arXiv:1605.06531] [INSPIRE]. · Zbl 1390.81578 · doi:10.1007/JHEP08(2016)059 |
| [7] | A. Cabo-Bizet, Factorising the 3D Topologically Twisted Index, JHEP04 (2017) 115 [arXiv:1606.06341] [INSPIRE]. · Zbl 1378.81136 · doi:10.1007/JHEP04(2017)115 |
| [8] | R. Emparan, AdS/CFT duals of topological black holes and the entropy of zero energy states, JHEP06 (1999) 036 [hep-th/9906040] [INSPIRE]. · Zbl 0951.83021 · doi:10.1088/1126-6708/1999/06/036 |
| [9] | S.L. Cacciatori, D. Klemm, D.S. Mansi and E. Zorzan, All timelike supersymmetric solutions of N = 2, D = 4 gauged supergravity coupled to abelian vector multiplets, JHEP05 (2008) 097 [arXiv:0804.0009] [INSPIRE]. · doi:10.1088/1126-6708/2008/05/097 |
| [10] | S.L. Cacciatori and D. Klemm, Supersymmetric AdS4black holes and attractors, JHEP01 (2010) 085 [arXiv:0911.4926] [INSPIRE]. · Zbl 1269.81110 · doi:10.1007/JHEP01(2010)085 |
| [11] | K. Hristov and S. Vandoren, Static supersymmetric black holes in AdS4with spherical symmetry, JHEP04 (2011) 047 [arXiv:1012.4314] [INSPIRE]. · Zbl 1250.83041 · doi:10.1007/JHEP04(2011)047 |
| [12] | N. Halmagyi, M. Petrini and A. Zaffaroni, BPS black holes in AdS4from M-theory, JHEP08 (2013) 124 [arXiv:1305.0730] [INSPIRE]. · Zbl 1342.83168 · doi:10.1007/JHEP08(2013)124 |
| [13] | N. Halmagyi, BPS Black Hole Horizons in N = 2 Gauged Supergravity, JHEP02 (2014) 051 [arXiv:1308.1439] [INSPIRE]. · doi:10.1007/JHEP02(2014)051 |
| [14] | A. Sen, Quantum Entropy Function from AdS2/CFT1Correspondence, Int. J. Mod. Phys.A 24 (2009) 4225 [arXiv:0809.3304] [INSPIRE]. · Zbl 1175.83045 · doi:10.1142/S0217751X09045893 |
| [15] | A. Dabholkar, J. Gomes and S. Murthy, Quantum black holes, localization and the topological string, JHEP06 (2011) 019 [arXiv:1012.0265] [INSPIRE]. · Zbl 1298.81261 · doi:10.1007/JHEP06(2011)019 |
| [16] | A. Faraggi and L.A. Pando Zayas, The Spectrum of Excitations of Holographic Wilson Loops, JHEP05 (2011) 018 [arXiv:1101.5145] [INSPIRE]. · Zbl 1296.81059 · doi:10.1007/JHEP05(2011)018 |
| [17] | E.I. Buchbinder and A.A. Tseytlin, 1/N correction in the D3-brane description of a circular Wilson loop at strong coupling, Phys. Rev.D 89 (2014) 126008 [arXiv:1404.4952] [INSPIRE]. |
| [18] | J.R. David, E. Gava, R.K. Gupta and K. Narain, Localization on AdS2× S1, JHEP03 (2017) 050 [arXiv:1609.07443] [INSPIRE]. · Zbl 1377.58021 · doi:10.1007/JHEP03(2017)050 |
| [19] | B. Assel, D. Martelli, S. Murthy and D. Yokoyama, Localization of supersymmetric field theories on non-compact hyperbolic three-manifolds, JHEP03 (2017) 095 [arXiv:1609.08071] [INSPIRE]. · Zbl 1377.81194 · doi:10.1007/JHEP03(2017)095 |
| [20] | V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun. Math. Phys.313 (2012) 71 [arXiv:0712.2824] [INSPIRE]. · Zbl 1257.81056 · doi:10.1007/s00220-012-1485-0 |
| [21] | K. Hosomichi, A review on SUSY gauge theories onS3, in New Dualities of Supersymmetric Gauge Theories, J. Teschner ed., pp. 307-338, (2016), [arXiv:1412.7128] [https://doi.org/10.1007/978-3-319-18769-3_10]. · Zbl 1334.81069 |
| [22] | S. Cremonesi, An Introduction to Localisation and Supersymmetry in Curved Space, PoS(Modave 2013)002. · Zbl 1388.81360 |
| [23] | O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP10 (2008) 091 [arXiv:0806.1218] [INSPIRE]. · Zbl 1245.81130 · doi:10.1088/1126-6708/2008/10/091 |
| [24] | 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, JHEP11 (2011) 143 [arXiv:1106.0080] [INSPIRE]. · Zbl 1306.83038 · doi:10.1007/JHEP11(2011)143 |
| [25] | A. Faraggi, W. Mueck and L.A. Pando Zayas, One-loop Effective Action of the Holographic Antisymmetric Wilson Loop, Phys. Rev.D 85 (2012) 106015 [arXiv:1112.5028] [INSPIRE]. |
| [26] | A. Sen, Entropy Function and AdS2/CFT1Correspondence, JHEP11 (2008) 075 [arXiv:0805.0095] [INSPIRE]. · doi:10.1088/1126-6708/2008/11/075 |
| [27] | G.V. Dunne, Aspects of Chern-Simons theory, in Topological Aspects of Low-dimensional Systems: Proceedings, Les Houches Summer School of Theoretical Physics, Session 69: Les Houches, France, July 7-31 1998, (1998), [hep-th/9902115] [INSPIRE]. · Zbl 0990.81107 |
| [28] | A. Kapustin, B. Willett and I. Yaakov, Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter, JHEP03 (2010) 089 [arXiv:0909.4559] [INSPIRE]. · Zbl 1271.81110 · doi:10.1007/JHEP03(2010)089 |
| [29] | R. Camporesi and A. Higuchi, Spectral functions and zeta functions in hyperbolic spaces, J. Math. Phys.35 (1994) 4217 [INSPIRE]. · Zbl 0811.58061 · doi:10.1063/1.530850 |
| [30] | A. Comtet, On the Landau Levels on the Hyperbolic Plane, Annals Phys.173 (1987) 185 [INSPIRE]. · Zbl 0635.58034 · doi:10.1016/0003-4916(87)90098-4 |
| [31] | M. Antoine, A. Comtet and S. Ouvry, Scattering on an Hyperbolic Torus in a Constant Magnetic Field, J. Phys.A 23 (1990) 3699 [INSPIRE]. · Zbl 0709.58041 |
| [32] | O. Lisovyy, Aharonov-Bohm effect on the Poincaré disk, J. Math. Phys.48 (2007) 052112 [math-ph/0702066] [INSPIRE]. · Zbl 1144.81379 |
| [33] | A. Almheiri and J. Polchinski, Models of AdS2backreaction and holography, JHEP11 (2015) 014 [arXiv:1402.6334] [INSPIRE]. · Zbl 1388.83079 · doi:10.1007/JHEP11(2015)014 |
| [34] | S. Sachdev, Bekenstein-Hawking Entropy and Strange Metals, Phys. Rev.X 5 (2015) 041025 [arXiv:1506.05111] [INSPIRE]. · doi:10.1103/PhysRevX.5.041025 |
| [35] | J. Maldacena and D. Stanford, Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev.D 94 (2016) 106002 [arXiv:1604.07818] [INSPIRE]. |
| [36] | J. Polchinski and V. Rosenhaus, The Spectrum in the Sachdev-Ye-Kitaev Model, JHEP04 (2016) 001 [arXiv:1601.06768] [INSPIRE]. · Zbl 1388.81067 · doi:10.1007/JHEP04(2016)001 |
| [37] | J. Maldacena, D. Stanford and Z. Yang, Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space, PTEP2016 (2016) 12C104 [arXiv:1606.01857] [INSPIRE]. · Zbl 1361.81112 |
| [38] | J. Engelsöy, T.G. Mertens and H. Verlinde, An investigation of AdS2backreaction and holography, JHEP07 (2016) 139 [arXiv:1606.03438] [INSPIRE]. · Zbl 1390.83104 · doi:10.1007/JHEP07(2016)139 |
| [39] | K. Jensen, Chaos in AdS2Holography, Phys. Rev. Lett.117 (2016) 111601 [arXiv:1605.06098] [INSPIRE]. · doi:10.1103/PhysRevLett.117.111601 |
| [40] | W. Fu, D. Gaiotto, J. Maldacena and S. Sachdev, Supersymmetric Sachdev-Ye-Kitaev models, Phys. Rev.D 95 (2017) 026009 [arXiv:1610.08917] [INSPIRE]. |
| [41] | R.K. Gupta and S. Murthy, All solutions of the localization equations for N = 2 quantum black hole entropy, JHEP02 (2013) 141 [arXiv:1208.6221] [INSPIRE]. · Zbl 1342.83027 · doi:10.1007/JHEP02(2013)141 |
| [42] | P. Goddard, J. Nuyts and D.I. Olive, Gauge Theories and Magnetic Charge, Nucl. Phys.B 125 (1977) 1 [INSPIRE]. · doi:10.1016/0550-3213(77)90221-8 |
| [43] | M. Nakahara, Geometry, topology and physics, Graduate student series in physics, Hilger, Bristol, U.S.A. (1990). · Zbl 0764.53001 |
| [44] | E. Witten, Supersymmetric index of three-dimensional gauge theory, hep-th/9903005 [INSPIRE]. · Zbl 0996.81061 |
| [45] | X. Huang, S.-J. Rey and Y. Zhou, Three-dimensional SCFT on conic space as hologram of charged topological black hole, JHEP03 (2014) 127 [arXiv:1401.5421] [INSPIRE]. · doi:10.1007/JHEP03(2014)127 |
| [46] | L. Andrianopoli et al., N = 2 supergravity and N = 2 super Yang-Mills theory on general scalar manifolds: Symplectic covariance, gaugings and the momentum map, J. Geom. Phys.23 (1997) 111 [hep-th/9605032] [INSPIRE]. · Zbl 0899.53073 · doi:10.1016/S0393-0440(97)00002-8 |
| [47] | A.H. Chamseddine and W.A. Sabra, Magnetic strings in five-dimensional gauged supergravity theories, Phys. Lett.B 477 (2000) 329 [hep-th/9911195] [INSPIRE]. · Zbl 0960.83037 · doi:10.1016/S0370-2693(00)00178-7 |
| [48] | D. Klemm and W.A. Sabra, Supersymmetry of black strings in D = 5 gauged supergravities, Phys. Rev.D 62 (2000) 024003 [hep-th/0001131] [INSPIRE]. |
| [49] | S. Banerjee, R.K. Gupta and A. Sen, Logarithmic Corrections to Extremal Black Hole Entropy from Quantum Entropy Function, JHEP03 (2011) 147 [arXiv:1005.3044] [INSPIRE]. · Zbl 1301.81182 · doi:10.1007/JHEP03(2011)147 |
| [50] | P. Benincasa and S. Nampuri, An SLE approach to four dimensional black hole microstate entropy, arXiv:1701.01864 [INSPIRE]. · Zbl 1250.83041 |
| [51] | F. Benini, K. Hristov and A. Zaffaroni, Exact microstate counting for dyonic black holes in AdS4, Phys. Lett.B 771 (2017) 462 [arXiv:1608.07294] [INSPIRE]. · Zbl 1372.83030 · doi:10.1016/j.physletb.2017.05.076 |
| [52] | S. Pasquetti, Factorisation of N = 2 Theories on the Squashed 3-Sphere, JHEP04 (2012) 120 [arXiv:1111.6905] [INSPIRE]. · Zbl 1348.81430 · doi:10.1007/JHEP04(2012)120 |
| [53] | E. Gava, K.S. Narain, M.N. Muteeb and V.I. Giraldo-Rivera, N = 2 gauge theories on the hemisphere HS4, Nucl. Phys.B 920 (2017) 256 [arXiv:1611.04804] [INSPIRE]. · Zbl 1364.81184 · doi:10.1016/j.nuclphysb.2017.04.007 |
| [54] | K. Hori and M. Romo, Exact Results In Two-Dimensional (2,2) Supersymmetric Gauge Theories With Boundary, arXiv:1308.2438 [INSPIRE]. · Zbl 1388.81360 |
| [55] | F. Nieri and S. Pasquetti, Factorisation and holomorphic blocks in 4d, JHEP11 (2015) 155 [arXiv:1507.00261] [INSPIRE]. · Zbl 1388.81360 · doi:10.1007/JHEP11(2015)155 |
| [56] | M. Honda and Y. Yoshida, Supersymmetric index on T2× S2and elliptic genus, arXiv:1504.04355 [INSPIRE]. · Zbl 1388.83388 |
| [57] | S.M. Hosseini, A. Nedelin and A. Zaffaroni, The Cardy limit of the topologically twisted index and black strings in AdS5, JHEP04 (2017) 014 [arXiv:1611.09374] [INSPIRE]. · Zbl 1378.81125 · doi:10.1007/JHEP04(2017)014 |
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