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Lectures on black holes and the AdS3/CFT2 correspondence. (English) Zbl 1155.83303

Bellucci, Stefano (ed.), Supersymmetric mechanics. Vol. 3: Attractors and black holes in supersymmetric gravity. Berlin: Springer (ISBN 978-3-540-79522-3/hbk). Lecture Notes in Physics 755, 193-247 (2008).
Summary: We present a detailed discussion of \(\text{AdS}_3\) black holes and their connection to two-dimensional conformal field theories via the AdS/CFT correspondence. Our emphasis is on deriving refined versions of black hole partition functions that include the effect of higher derivative terms in the spacetime action as well as non-perturbative effects. We include background material on gravity in \(\text{AdS}_3\), in the context of holographic renormalization.
For the entire collection see [Zbl 1146.83003].

MSC:

83-02 Research exposition (monographs, survey articles) pertaining to relativity and gravitational theory
83C57 Black holes
83C80 Analogues of general relativity in lower dimensions
83E30 String and superstring theories in gravitational theory
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[1] Strominger, A.; Vafa, C., Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett. B, 379, 99 (1996) · Zbl 1376.83026 · doi:10.1016/0370-2693(96)00345-0
[2] Maldacena, J. M., The large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys., 2, 231 (1998) · Zbl 0914.53047
[3] Maldacena, J. M., The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys., 38, 1113 (1999) · Zbl 0969.81047 · doi:10.1023/A:1026654312961
[4] R. Emparan and G. T. Horowitz, “Microstates of a neutral black hole in M theory,” arXiv:hep-th/0607023.
[5] Banados, M.; Teitelboim, C.; Zanelli, J., The Black hole in three-dimensional space-time, Phys. Rev. Lett., 69, 1849 (1992) · Zbl 0968.83514 · doi:10.1103/PhysRevLett.69.1849
[6] Banados, M.; Henneaux, M.; Teitelboim, C.; Zanelli, J., Geometry of the (2+1) black hole, Phys. Rev. D, 48, 1506 (1993) · doi:10.1103/PhysRevD.48.1506
[7] Dabholkar, A.; Denef, F.; Moore, G. W.; Pioline, B., Exact and asymptotic degeneracies of small black holes, JHEP, 0508, 021 (2005) · doi:10.1088/1126-6708/2005/08/021
[8] Dabholkar, A.; Denef, F.; Moore, G. W.; Pioline, B., Precision counting of small black holes, JHEP, 0510, 096 (2005) · doi:10.1088/1126-6708/2005/10/096
[9] Brown, J. D.; Henneaux, M., Central charges in the canonical realization of asymptotic symmetries: An example from three-dimensional gravity, Commun. Math. Phys., 104, 207 (1986) · Zbl 0584.53039 · doi:10.1007/BF01211590
[10] R. Dijkgraaf, J. M. Maldacena, G. W. Moore and E. P. Verlinde, “A black hole farey tail,” arXiv:hep-th/0005003.
[11] D. Gaiotto, A. Strominger and X. Yin, “From AdS(3)/CFT(2) to black holes/topological strings,” arXiv:hep-th/0602046.
[12] Ooguri, H.; Strominger, A.; Vafa, C., Black hole attractors and the topological string, Phys. Rev. D, 70, 106007 (2004) · doi:10.1103/PhysRevD.70.106007
[13] Kraus, P.; Larsen, F., Microscopic black hole entropy in theories with higher derivatives, JHEP, 0509, 034 (2005) · doi:10.1088/1126-6708/2005/09/034
[14] P. Kraus and F. Larsen, “Partition functions and elliptic genera from supergravity,” arXiv:hep-th/0607138.
[15] J. M. Maldacena, “Black holes in string theory,” arXiv:hep-th/9607235. · Zbl 1192.83058
[16] Aharony, O.; Gubser, S. S.; Maldacena, J. M.; Ooguri, H.; Oz, Y., Large N field theories, string theory and gravity, Phys. Rep., 323, 183 (2000) · Zbl 1368.81009 · doi:10.1016/S0370-1573(99)00083-6
[17] Mohaupt, T., Black hole entropy, special geometry and strings, Fortsch. Phys., 49, 3 (2001) · Zbl 0985.83001 · doi:10.1002/1521-3978(200102)49:1/3<3::AID-PROP3>3.0.CO;2-#
[18] A. W. Peet, “TASI lectures on black holes in string theory,” arXiv:hep-th/0008241. · Zbl 1004.83002
[19] David, J. R.; Mandal, G.; Wadia, S. R., Microscopic formulation of black holes in string theory, Phys. Rep., 369, 549 (2002) · Zbl 0998.83032 · doi:10.1016/S0370-1573(02)00271-5
[20] Mathur, S. D., The quantum structure of black holes, Class. Quant. Grav., 23, R115 (2006) · Zbl 1101.83032 · doi:10.1088/0264-9381/23/11/R01
[21] B. Pioline, “Lectures on on black holes, topological strings and quantum attractors,” arXiv:hep-th/0607227. · Zbl 1155.83305
[22] Brown, J. D.; York, J. W., Quasilocal energy and conserved charges derived from the gravitational, Phys. Rev. D, 47, 1407 (1993) · doi:10.1103/PhysRevD.47.1407
[23] C. Fefferman and C.R. Graham, “Conformal invariants”, in Elie Cartan et les Mathématiques d’aujourd’hui (Astérisque, 1985) 95. · Zbl 0602.53007
[24] de Haro, S.; Solodukhin, S. N.; Skenderis, K., Holographic reconstruction of spacetime and renormalization in the AdS/CFT correspondence, Commun. Math. Phys., 217, 595 (2001) · Zbl 0984.83043 · doi:10.1007/s002200100381
[25] Henningson, M.; Skenderis, K., The holographic Weyl anomaly, JHEP, 9807, 023 (1998) · Zbl 0958.81083 · doi:10.1088/1126-6708/1998/07/023
[26] Balasubramanian, V.; Kraus, P., A stress tensor for anti-de Sitter gravity, Commun. Math. Phys., 208, 413 (1999) · Zbl 0946.83013 · doi:10.1007/s002200050764
[27] Emparan, R.; Johnson, C. V.; Myers, R. C., Surface terms as counterterms in the AdS/CFT correspondence, Phys. Rev. D, 60, 104001 (1999) · doi:10.1103/PhysRevD.60.104001
[28] Kraus, P.; Larsen, F.; Siebelink, R., The gravitational action in asymptotically AdS and flat spacetimes, Nucl. Phys. B, 563, 259 (1999) · Zbl 0953.83040 · doi:10.1016/S0550-3213(99)00549-0
[29] I. Papadimitriou and K. Skenderis, “Thermodynamics of asymptotically locally AdS spacetimes,” arXiv:hep-th/0505190. · Zbl 1081.81085
[30] Hollands, S.; Ishibashi, A.; Marolf, D., Comparison between various notions of conserved charges in asymptotically AdS-spacetimes, Class. Quant. Grav., 22, 2881 (2005) · Zbl 1082.83014 · doi:10.1088/0264-9381/22/14/004
[31] S. Hollands, A. Ishibashi and D. Marolf, “Counter-term charges generate bulk symmetries,” arXiv:hep-th/0503105. · Zbl 1082.83014
[32] Nojiri, S.; Odintsov, S. D., Conformal anomaly for dilaton coupled theories from AdS/CFT correspondence, Phys. Lett. B, 444, 92 (1998) · doi:10.1016/S0370-2693(98)01351-3
[33] Imbimbo, C.; Schwimmer, A.; Theisen, S.; Yankielowicz, S., Diffeomorphisms and holographic anomalies, Class. Quant. Grav., 17, 1129 (2000) · Zbl 0952.81052 · doi:10.1088/0264-9381/17/5/322
[34] Saida, H.; Soda, J., Statistical entropy of BTZ black hole in higher curvature gravity, Phys. Lett. B, 471, 358 (2000) · Zbl 0974.83030 · doi:10.1016/S0370-2693(99)01405-7
[35] Wald, R. M., Black hole entropy is the Noether charge, Phys. Rev. D, 48, 3427 (1993) · Zbl 0942.83512 · doi:10.1103/PhysRevD.48.R3427
[36] Wald, R., Phys. Rev. D, 48, R3427 (1993) · Zbl 0942.83512 · doi:10.1103/PhysRevD.48.R3427
[37] Iyer, V.; Wald, R. M., Some properties of Noether charge and a proposal for dynamical black hole entropy, Phys. Rev. D, 50, 846 (1994)
[38] Iyer, V.; Wald, R. M., A comparison of noether charge and euclidean methods for computing the entropy of stationary black holes, Phys. Rev. D, 52, 4430 (1995) · doi:10.1103/PhysRevD.52.4430
[39] Carlip, S.; Teitelboim, C., Aspects of black hole quantum mechanics and thermodynamics in (2+1)-dimensions, Phys. Rev. D, 51, 622 (1995) · doi:10.1103/PhysRevD.51.622
[40] Maldacena, J. M.; Strominger, A., AdS(3) black holes and a stringy exclusion principle, JHEP, 9812, 005 (1998) · Zbl 0951.83019 · doi:10.1088/1126-6708/1998/12/005
[41] Elitzur, S.; Moore, G. W.; Schwimmer, A.; Seiberg, N., Remarks on the canonical quantization of the chern-simons-witten theory, Nucl. Phys. B, 326, 108 (1989) · doi:10.1016/0550-3213(89)90436-7
[42] S. Gukov, E. Martinec, G. W. Moore and A. Strominger, “Chern-Simons gauge theory and the AdS(3)/CFT(2) correspondence,” arXiv:hep-th/0403225.
[43] Freed, D.; Harvey, J. A.; Minasian, R.; Moore, G. W., Gravitational anomaly cancellation for M-theory fivebranes, Adv. Theor. Math. Phys., 2, 601 (1998) · Zbl 0971.81152
[44] Harvey, J. A.; Minasian, R.; Moore, G. W., Non-abelian tensor-multiplet anomalies, JHEP, 9809, 004 (1998) · Zbl 0953.81093 · doi:10.1088/1126-6708/1998/09/004
[45] J. Hansen and P. Kraus, “Generating charge from diffeomorphisms,” arXiv:hep-th/0606230. · Zbl 1226.83062
[46] Kraus, P.; Larsen, F., Holographic gravitational anomalies, JHEP, 0601, 022 (2006) · doi:10.1088/1126-6708/2006/01/022
[47] Alvarez-Gaume, L.; Witten, E., Gravitational anomalies, Nucl. Phys. B, 234, 269 (1984) · doi:10.1016/0550-3213(84)90066-X
[48] Bardeen, W. A.; Zumino, B., Consistent and covariant anomalies in gauge and gravitational theories, Nucl. Phys. B, 244, 421 (1984) · doi:10.1016/0550-3213(84)90322-5
[49] P. H. Ginsparg, “Applications of topological and differential geometric methods to anomalies in quantum field theory,” HUTP-85/A056 To appear in Proc. of 16th GIFT Seminar on Theoretical Physics, Jaca, Spain, Jun 3-7, (1985)
[50] Deser, S.; Jackiw, R.; Templeton, S., Topologically massive gauge theories, Annals Phys., 140, 372 (1982) · doi:10.1016/0003-4916(82)90164-6
[51] Deser, S.; Jackiw, R.; Templeton, S., Topologically Massive Gauge Theories, Annals Phys. (Erratum) Erratum., 185, 406 (1988)
[52] Deser, S.; Jackiw, R.; Templeton, S., Three-dimensional massive gauge theories, Phys. Rev. Lett., 48, 975 (1982) · doi:10.1103/PhysRevLett.48.975
[53] Solodukhin, S. N., Holography with gravitational chern-simons, Phys. Rev. D, 74, 024015 (2006) · doi:10.1103/PhysRevD.74.024015
[54] Solodukhin, S. N., Holographic description of gravitational anomalies, JHEP, 0607, 003 (2006) · doi:10.1088/1126-6708/2006/07/003
[55] Maldacena, J. M.; Strominger, A.; Witten, E., JHEP, 9712, 002 (1997) · Zbl 0951.83034 · doi:10.1088/1126-6708/1997/12/002
[56] Callan, C. G.; Harvey, J. A., Anomalies and fermion zero modes on strings and domain walls, Nucl. Phys. B, 250, 427 (1985) · doi:10.1016/0550-3213(85)90489-4
[57] Cvetic, M.; Larsen, F., Near horizon geometry of rotating black holes in five dimensions, Nucl. Phys. B, 531, 239 (1998) · Zbl 0956.83033 · doi:10.1016/S0550-3213(98)00604-X
[58] Balasubramanian, V.; de Boer, J.; Keski-Vakkuri, E.; Ross, S. F., Supersymmetric conical defects: Towards a string theoretic description of black hole formation, Phys. Rev. D, 64, 064011 (2001) · doi:10.1103/PhysRevD.64.064011
[59] Maldacena, J. M.; Maoz, L., De-singularization by rotation, JHEP, 0212, 055 (2002) · doi:10.1088/1126-6708/2002/12/055
[60] O. Lunin, J. M. Maldacena and L. Maoz, “Gravity solutions for the D1-D5 system with angular momentum,” arXiv:hep-th/0212210;
[61] Minasian, R.; Moore, G. W.; Tsimpis, D., Calabi-Yau black holes and (0,4) sigma models, Commun. Math. Phys., 209, 325 (2000) · Zbl 0960.83022
[62] Green, M. B.; Schwarz, J. H., Supersymmetrical Dual String Theory. 2. Vertices and Trees, Nucl. Phys. B, 198, 252 (1982) · doi:10.1016/0550-3213(82)90556-9
[63] Gross, D. J.; Witten, E., Superstring modifications of einstein’s equations, Nucl. Phys. B, 277, 1 (1986) · doi:10.1016/0550-3213(86)90429-3
[64] Lerche, W.; Nilsson, B. E.W.; Schellekens, A. N., Heterotic string loop calculation of the anomaly cancelling term, Nucl. Phys. B, 289, 609 (1987) · doi:10.1016/0550-3213(87)90397-X
[65] Duff, M. J.; Liu, J. T.; Minasian, R., Eleven-dimensional origin of string/string duality: A one-loop test, Nucl. Phys. B, 452, 261 (1995) · Zbl 0925.81148 · doi:10.1016/0550-3213(95)00368-3
[66] Green, M. B.; Gutperle, M.; Vanhove, P., One loop in eleven dimensions, Phys. Lett. B, 409, 177 (1997) · doi:10.1016/S0370-2693(97)00931-3
[67] Russo, J. G.; Tseytlin, A. A., One-loop four-graviton amplitude in eleven-dimensional supergravity, Nucl. Phys. B, 508, 245 (1997) · Zbl 0925.83112 · doi:10.1016/S0550-3213(97)00631-7
[68] Howe, P. S.; Tsimpis, D., On higher-order corrections in M theory, JHEP, 0309, 038 (2003) · doi:10.1088/1126-6708/2003/09/038
[69] Tseytlin, A. A., R^**4 terms in 11 dimensions and conformal anomaly of (2,0) theory, Nucl. Phys. B, 584, 233 (2000) · Zbl 0984.81147 · doi:10.1016/S0550-3213(00)00380-1
[70] Antoniadis, I.; Ferrara, S.; Minasian, R.; Narain, K. S., R^**4 couplings in M- and type II theories on Calabi-Yau spaces, Nucl. Phys. B, 507, 571 (1997) · Zbl 0925.14024 · doi:10.1016/S0550-3213(97)00572-5
[71] Kraus, P.; Larsen, F., Attractors and black rings, Phys. Rev. D, 72, 024010 (2005) · doi:10.1103/PhysRevD.72.024010
[72] R. Bott and A.S. Cattaneo, “Integral invariant of 3-manifolds,” [arxiv:dg-ga/9710001]. · Zbl 0953.57008
[73] Lopes Cardoso, G.; de Wit, B.; Mohaupt, T., Macroscopic entropy formulae and non-holomorphic corrections for supersymmetric black holes”, Nucl. Phys. B, 567, 87 (2000) · Zbl 0951.81039 · doi:10.1016/S0550-3213(99)00560-X
[74] Lopes Cardoso, G.; de Wit, B.; Mohaupt, T., Deviations from the area law for supersymmetric black holes”, Fortsch. Phys., 48, 49 (2000) · Zbl 0952.83034 · doi:10.1002/(SICI)1521-3978(20001)48:1/3<49::AID-PROP49>3.0.CO;2-O
[75] Lopes Cardoso, G.; de Wit, B.; Mohaupt, T., Corrections to macroscopic supersymmetric black-hole entropy”, Phys. Lett. B, 451, 309 (1999) · Zbl 1058.83516 · doi:10.1016/S0370-2693(99)00227-0
[76] B. Sahoo and A. Sen, “Higher derivative corrections to non-supersymmetric extremal black holes in N=2 supergravity,” arXiv:hep-th/0603149.
[77] A. Dabholkar, “Exact counting of black hole microstates”, [arXiv:hep-th/0409148].
[78] Dabholkar, A.; Kallosh, R.; Maloney, A., A stringy cloak for a classical singularity”, JHEP, 0412, 059 (2004) · doi:10.1088/1126-6708/2004/12/059
[79] Sen, A., How does a fundamental string stretch its horizon?, JHEP, 0505, 059 (2005) · doi:10.1088/1126-6708/2005/05/059
[80] A. Sen, “Black holes, elementary strings and holomorphic anomaly,” arXiv:hep-th/0502126;
[81] A. Sen, “Stretching the horizon of a higher dimensional small black hole,” arXiv:hep-th/0505122.
[82] “Black hole entropy function and the attractor mechanism in higher derivative gravity,” arXiv:hep-th/0506177.
[83] “Entropy function for heterotic black holes,” arXiv:hep-th/0508042. · Zbl 1226.83037
[84] J. Polchinski, “String theory” · Zbl 1080.81582
[85] Kawai, T.; Yamada, Y.; Yang, S. K., Elliptic genera and N=2 superconformal field theory, Nucl. Phys. B, 414, 191 (1994) · Zbl 0980.58500 · doi:10.1016/0550-3213(94)90428-6
[86] G. W. Moore, “Les Houches lectures on strings and arithmetic,” arXiv:hep-th/0401049.
[87] J. de Boer, M. C. N. Cheng, R. Dijkgraaf, J. Manschot and E. Verlinde, “A farey tail for attractor black holes,” arXiv:hep-th/0608059.
[88] O. Lunin, J. M. Maldacena and L. Maoz, “Gravity solutions for the D1-D5 system with angular momentum,” arXiv:hep-th/0212210.
[89] Mathur, S. D., The fuzzball proposal for black holes: An elementary review, Fortsch. Phys., 53, 793 (2005) · Zbl 1116.83300 · doi:10.1002/prop.200410203
[90] Goldstein, K.; Iizuka, N.; Jena, R. P.; Trivedi, S. P., Non-supersymmetric attractors, Phys. Rev. D, 72, 124021 (2005) · doi:10.1103/PhysRevD.72.124021
[91] Kutasov, D.; Larsen, F.; Leigh, R. G., String theory in magnetic monopole backgrounds, Nucl. Phys. B, 550, 183 (1999) · Zbl 0947.81078 · doi:10.1016/S0550-3213(99)00144-3
[92] Larsen, F., The perturbation spectrum of black holes in N=8 supergravity, Nucl. Phys. B, 536, 258 (1998) · Zbl 0940.83031 · doi:10.1016/S0550-3213(98)00564-1
[93] de Boer, J., Six-dimensional supergravity on S^**3 x AdS(3) and 2d conformal field theory, Nucl. Phys. B, 548, 139 (1999) · Zbl 0944.83032 · doi:10.1016/S0550-3213(99)00160-1
[94] R. Gopakumar and C. Vafa, “M-theory and topological strings. I,” arXiv:hep-th/9809187. · Zbl 0922.32015
[95] R. Gopakumar and C. Vafa, “M-theory and topological strings. II,” arXiv:hep-th/9812127. · Zbl 0922.32015
[96] de Boer, J., Large N elliptic genus and AdS/CFT correspondence, JHEP, 9905, 017 (1999) · Zbl 1017.81041 · doi:10.1088/1126-6708/1999/05/017
[97] Bena, I.; Warner, N. P., Black Holes, Black Rings and their Microstates, Lect. Notes. Phys., 755, x-xx (2008) · Zbl 1155.83301
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