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New boundary conditions for \(\mathrm{AdS}_2\). (English) Zbl 1457.83042

Summary: We describe new boundary conditions for \(\mathrm{AdS}_2\) in Jackiw-Teitelboim gravity. The asymptotic symmetry group is enhanced to \(\mathrm{Diff} (S^1) \ltimes C^\infty (S^1)\) whose breaking to \(\mathrm{SL} (2, \mathbb{R}) \times \mathrm{U}(1)\) controls the near-\(\mathrm{AdS}_2\) dynamics. The action reduces to a boundary term which is a generalization of the Schwarzian theory and can be interpreted as the coadjoint action of the warped Virasoro group. This theory reproduces the low-energy effective action of the complex SYK model. We compute the Euclidean path integral and derive its relation to the random matrix ensemble of Saad, Shenker and Stanford. We study the flat space version of this action, and show that the corresponding path integral also gives an ensemble average, but of a much simpler nature. We explore some applications to near-extremal black holes.

MSC:

83C80 Analogues of general relativity in lower dimensions
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
83C45 Quantization of the gravitational field
83C57 Black holes
81S40 Path integrals in quantum mechanics
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations
81R40 Symmetry breaking in quantum theory
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[1] Maldacena, JM, 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
[2] Ferrara, S.; Kallosh, R.; Strominger, A., N = 2 extremal black holes, Phys. Rev. D, 52, 5412 (1995) · doi:10.1103/PhysRevD.52.R5412
[3] Ferrara, S.; Kallosh, R., Supersymmetry and attractors, Phys. Rev. D, 54, 1514 (1996) · Zbl 1171.83329 · doi:10.1103/PhysRevD.54.1514
[4] Ferrara, S.; Kallosh, R., Universality of supersymmetric attractors, Phys. Rev. D, 54, 1525 (1996) · Zbl 1171.83330 · doi:10.1103/PhysRevD.54.1525
[5] Astefanesei, D.; Goldstein, K.; Jena, RP; Sen, A.; Trivedi, SP, Rotating attractors, JHEP, 10, 058 (2006) · doi:10.1088/1126-6708/2006/10/058
[6] Kunduri, HK; Lucietti, J.; Reall, HS, Near-horizon symmetries of extremal black holes, Class. Quant. Grav., 24, 4169 (2007) · Zbl 1205.83047 · doi:10.1088/0264-9381/24/16/012
[7] H.K. Kunduri and J. Lucietti, Uniqueness of near-horizon geometries of rotating extremal AdS_4black holes, Class. Quant. Grav.26 (2009) 055019 [arXiv:0812.1576] [INSPIRE]. · Zbl 1160.83334
[8] Kunduri, HK; Lucietti, J., Classification of near-horizon geometries of extremal black holes, Living Rev. Rel., 16, 8 (2013) · Zbl 1320.83005 · doi:10.12942/lrr-2013-8
[9] Strominger, A., Black hole entropy from near horizon microstates, JHEP, 02, 009 (1998) · Zbl 0955.83010 · doi:10.1088/1126-6708/1998/02/009
[10] Maldacena, JM; Strominger, A., AdS_3black holes and a stringy exclusion principle, JHEP, 12, 005 (1998) · Zbl 0951.83019 · doi:10.1088/1126-6708/1998/12/005
[11] Strominger, A., AdS_2quantum gravity and string theory, JHEP, 01, 007 (1999) · Zbl 0965.81097 · doi:10.1088/1126-6708/1999/01/007
[12] Sen, A., Entropy function and AdS_2/CFT_1correspondence, JHEP, 11, 075 (2008) · doi:10.1088/1126-6708/2008/11/075
[13] Sen, A., Quantum entropy function from AdS_2/CFT_1correspondence, Int. J. Mod. Phys. A, 24, 4225 (2009) · Zbl 1175.83045 · doi:10.1142/S0217751X09045893
[14] Maldacena, JM; Michelson, J.; Strominger, A., Anti-de Sitter fragmentation, JHEP, 02, 011 (1999) · Zbl 0956.83052 · doi:10.1088/1126-6708/1999/02/011
[15] Almheiri, A.; Polchinski, J., Models of AdS_2backreaction and holography, JHEP, 11, 014 (2015) · Zbl 1388.83079 · doi:10.1007/JHEP11(2015)014
[16] 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
[17] Jensen, K., Chaos in AdS_2holography, Phys. Rev. Lett., 117, 111601 (2016) · doi:10.1103/PhysRevLett.117.111601
[18] Engelsöy, J.; Mertens, TG; Verlinde, H., An investigation of AdS_2backreaction and holography, JHEP, 07, 139 (2016) · Zbl 1390.83104 · doi:10.1007/JHEP07(2016)139
[19] Maldacena, J.; Stanford, D., Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev. D, 94, 106002 (2016) · doi:10.1103/PhysRevD.94.106002
[20] Jackiw, R., Lower dimensional gravity, Nucl. Phys. B, 252, 343 (1985) · doi:10.1016/0550-3213(85)90448-1
[21] Teitelboim, C., Gravitation and Hamiltonian structure in two space-time dimensions, Phys. Lett. B, 126, 41 (1983) · doi:10.1016/0370-2693(83)90012-6
[22] S. Sachdev and J. Ye, Gapless spin fluid ground state in a random, quantum Heisenberg magnet, Phys. Rev. Lett.70 (1993) 3339 [cond-mat/9212030] [INSPIRE].
[23] A. Kitaev, A simple model of quantum holography (part 1), talk at KITP, http://online.kitp.ucsb.edu/online/entangled15/kitaev/, University of California, Santa Barbara, CA, U.S.A., 7 April 2015.
[24] A. Kitaev, A simple model of quantum holography (part 2), talk at KITP, http://online.kitp.ucsb.edu/online/entangled15/kitaev2/, University of California, Santa Barbara, CA, U.S.A., 27 May 2015.
[25] Stanford, D.; Witten, E., Fermionic localization of the Schwarzian theory, JHEP, 10, 008 (2017) · Zbl 1383.83099 · doi:10.1007/JHEP10(2017)008
[26] Duistermaat, JJ; Heckman, GJ, On the variation in the cohomology of the symplectic form of the reduced phase space, Invent. Math., 69, 259 (1982) · Zbl 0503.58015 · doi:10.1007/BF01399506
[27] Maldacena, JM, Eternal black holes in anti-de Sitter, JHEP, 04, 021 (2003) · doi:10.1088/1126-6708/2003/04/021
[28] Papadodimas, K.; Raju, S., Local operators in the eternal black hole, Phys. Rev. Lett., 115, 211601 (2015) · doi:10.1103/PhysRevLett.115.211601
[29] J.S. Cotler et al., Black holes and random matrices, JHEP05 (2017) 118 [Erratum ibid.09 (2018) 002] [arXiv:1611.04650] [INSPIRE]. · Zbl 1380.81307
[30] P. Saad, S.H. Shenker and D. Stanford, A semiclassical ramp in SYK and in gravity, arXiv:1806.06840 [INSPIRE].
[31] P. Saad, S.H. Shenker and D. Stanford, JT gravity as a matrix integral, arXiv:1903.11115 [INSPIRE].
[32] D. Stanford and E. Witten, JT gravity and the ensembles of random matrix theory, arXiv:1907.03363 [INSPIRE].
[33] L.V. Iliesiu, On 2D gauge theories in Jackiw-Teitelboim gravity, arXiv:1909.05253 [INSPIRE].
[34] Kapec, D.; Mahajan, R.; Stanford, D., Matrix ensembles with global symmetries and ’t Hooft anomalies from 2d gauge theory, JHEP, 04, 186 (2020) · Zbl 1436.83052 · doi:10.1007/JHEP04(2020)186
[35] Penington, G., Entanglement wedge reconstruction and the information paradox, JHEP, 09, 002 (2020) · Zbl 1454.81039 · doi:10.1007/JHEP09(2020)002
[36] Almheiri, A.; Engelhardt, N.; Marolf, D.; Maxfield, H., The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole, JHEP, 12, 063 (2019) · Zbl 1431.83123 · doi:10.1007/JHEP12(2019)063
[37] Ryu, S.; Takayanagi, T., Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett., 96, 181602 (2006) · Zbl 1228.83110 · doi:10.1103/PhysRevLett.96.181602
[38] Hubeny, VE; Rangamani, M.; Takayanagi, T., A covariant holographic entanglement entropy proposal, JHEP, 07, 062 (2007) · doi:10.1088/1126-6708/2007/07/062
[39] Engelhardt, N.; Wall, AC, Quantum extremal surfaces: holographic entanglement entropy beyond the classical regime, JHEP, 01, 073 (2015) · doi:10.1007/JHEP01(2015)073
[40] Faulkner, T.; Lewkowycz, A.; Maldacena, J., Quantum corrections to holographic entanglement entropy, JHEP, 11, 074 (2013) · Zbl 1392.81021 · doi:10.1007/JHEP11(2013)074
[41] Almheiri, A.; Mahajan, R.; Maldacena, J.; Zhao, Y., The Page curve of Hawking radiation from semiclassical geometry, JHEP, 03, 149 (2020) · Zbl 1435.83110 · doi:10.1007/JHEP03(2020)149
[42] A. Almheiri, R. Mahajan and J. Maldacena, Islands outside the horizon, arXiv:1910.11077 [INSPIRE]. · Zbl 1435.83110
[43] G. Penington, S.H. Shenker, D. Stanford and Z. Yang, Replica wormholes and the black hole interior, arXiv:1911.11977 [INSPIRE].
[44] Almheiri, A.; Hartman, T.; Maldacena, J.; Shaghoulian, E.; Tajdini, A., Replica wormholes and the entropy of Hawking radiation, JHEP, 05, 013 (2020) · Zbl 1437.83084 · doi:10.1007/JHEP05(2020)013
[45] Lewkowycz, A.; Maldacena, J., Generalized gravitational entropy, JHEP, 08, 090 (2013) · Zbl 1342.83185 · doi:10.1007/JHEP08(2013)090
[46] Dong, X.; Lewkowycz, A., Entropy, extremality, Euclidean variations, and the equations of motion, JHEP, 01, 081 (2018) · Zbl 1384.81097 · doi:10.1007/JHEP01(2018)081
[47] Grumiller, D.; McNees, R.; Salzer, J.; Valcárcel, C.; Vassilevich, D., Menagerie of AdS_2boundary conditions, JHEP, 10, 203 (2017) · Zbl 1383.83114 · doi:10.1007/JHEP10(2017)203
[48] González, HA; Grumiller, D.; Salzer, J., Towards a bulk description of higher spin SYK, JHEP, 05, 083 (2018) · Zbl 1391.83077 · doi:10.1007/JHEP05(2018)083
[49] Davison, RA; Fu, W.; Georges, A.; Gu, Y.; Jensen, K.; Sachdev, S., Thermoelectric transport in disordered metals without quasiparticles: the Sachdev-Ye-Kitaev models and holography, Phys. Rev. B, 95, 155131 (2017) · doi:10.1103/PhysRevB.95.155131
[50] Bulycheva, K., A note on the SYK model with complex fermions, JHEP, 12, 069 (2017) · Zbl 1383.81188 · doi:10.1007/JHEP12(2017)069
[51] Gu, Y.; Kitaev, A.; Sachdev, S.; Tarnopolsky, G., Notes on the complex Sachdev-Ye-Kitaev model, JHEP, 02, 157 (2020) · Zbl 1435.83154 · doi:10.1007/JHEP02(2020)157
[52] Guo, H.; Gu, Y.; Sachdev, S., Linear in temperature resistivity in the limit of zero temperature from the time reparameterization soft mode, Annals Phys., 418, 168202 (2020) · Zbl 1435.82034 · doi:10.1016/j.aop.2020.168202
[53] H. Afshar, H.A. González, D. Grumiller and D. Vassilevich, Flat space holography and the complex Sachdev-Ye-Kitaev model, Phys. Rev. D101 (2020) 086024 [arXiv:1911.05739] [INSPIRE].
[54] Detournay, S.; Hartman, T.; Hofman, DM, Warped conformal field theory, Phys. Rev. D, 86, 124018 (2012) · doi:10.1103/PhysRevD.86.124018
[55] Guica, M.; Hartman, T.; Song, W.; Strominger, A., The Kerr/CFT correspondence, Phys. Rev. D, 80, 124008 (2009) · doi:10.1103/PhysRevD.80.124008
[56] Aggarwal, A.; Castro, A.; Detournay, S., Warped symmetries of the Kerr black hole, JHEP, 01, 016 (2020) · Zbl 1434.83048 · doi:10.1007/JHEP01(2020)016
[57] Dias, OJC; Reall, HS; Santos, JE, Kerr-CFT and gravitational perturbations, JHEP, 08, 101 (2009) · doi:10.1088/1126-6708/2009/08/101
[58] Amsel, AJ; Horowitz, GT; Marolf, D.; Roberts, MM, No dynamics in the extremal Kerr throat, JHEP, 09, 044 (2009) · doi:10.1088/1126-6708/2009/09/044
[59] Chaturvedi, P.; Gu, Y.; Song, W.; Yu, B., A note on the complex SYK model and warped CFTs, JHEP, 12, 101 (2018) · Zbl 1405.81121 · doi:10.1007/JHEP12(2018)101
[60] Castro, A.; Godet, V., Breaking away from the near horizon of extreme Kerr, SciPost Phys., 8, 089 (2020) · doi:10.21468/SciPostPhys.8.6.089
[61] Dubovsky, S.; Gorbenko, V.; Mirbabayi, M., Asymptotic fragility, near AdS_2holography and \(T\overline{T} \), JHEP, 09, 136 (2017) · Zbl 1382.83076 · doi:10.1007/JHEP09(2017)136
[62] A. Laddha, S.G. Prabhu, S. Raju and P. Shrivastava, The holographic nature of null infinity, arXiv:2002.02448 [INSPIRE].
[63] Anegawa, T.; Iizuka, N., Notes on islands in asymptotically flat 2d dilaton black holes, JHEP, 07, 036 (2020) · Zbl 1451.83056 · doi:10.1007/JHEP07(2020)036
[64] Gautason, FF; Schneiderbauer, L.; Sybesma, W.; Thorlacius, L., Page curve for an evaporating black hole, JHEP, 05, 091 (2020) · Zbl 1437.83080 · doi:10.1007/JHEP05(2020)091
[65] Hartman, T.; Shaghoulian, E.; Strominger, A., Islands in asymptotically flat 2D gravity, JHEP, 07, 022 (2020) · Zbl 1455.83017 · doi:10.1007/JHEP07(2020)022
[66] C. Krishnan, V. Patil and J. Pereira, Page curve and the information paradox in flat space, arXiv:2005.02993 [INSPIRE].
[67] Barnich, G.; Troessaert, C., Aspects of the BMS/CFT correspondence, JHEP, 05, 062 (2010) · Zbl 1287.83043 · doi:10.1007/JHEP05(2010)062
[68] Kirillov, A., Lectures on the orbit method (2004), U.S.A.: American Mathematical Society, U.S.A. · Zbl 1229.22003 · doi:10.1090/gsm/064
[69] Afshar, H.; Detournay, S.; Grumiller, D.; Oblak, B., Near-horizon geometry and warped conformal symmetry, JHEP, 03, 187 (2016) · Zbl 1388.83362 · doi:10.1007/JHEP03(2016)187
[70] R.M. Wald, Black hole entropy is the Noether charge, Phys. Rev. D48 (1993) 3427 [gr-qc/9307038] [INSPIRE]. · Zbl 0942.83512
[71] V. Iyer and R.M. Wald, Some properties of Noether charge and a proposal for dynamical black hole entropy, Phys. Rev. D50 (1994) 846 [gr-qc/9403028] [INSPIRE].
[72] R.M. Wald and A. Zoupas, A general definition of ‘conserved quantities’ in general relativity and other theories of gravity, Phys. Rev. D61 (2000) 084027 [gr-qc/9911095] [INSPIRE]. · Zbl 1136.83317
[73] G. Compère and A. Fiorucci, Advanced lectures on general relativity, arXiv:1801.07064 [INSPIRE]. · Zbl 1419.83003
[74] Barnich, G.; Troessaert, C., BMS charge algebra, JHEP, 12, 105 (2011) · Zbl 1306.83002 · doi:10.1007/JHEP12(2011)105
[75] Donnay, L.; Giribet, G.; González, HA; Pino, M., Extended symmetries at the black hole horizon, JHEP, 09, 100 (2016) · Zbl 1390.83191 · doi:10.1007/JHEP09(2016)100
[76] Donnay, L.; Marteau, C., Carrollian physics at the black hole horizon, Class. Quant. Grav., 36, 165002 (2019) · Zbl 1477.83050 · doi:10.1088/1361-6382/ab2fd5
[77] R. Ruzziconi, Asymptotic symmetries in the gauge fixing approach and the BMS group, PoS(Modave2019)003 (2020) [arXiv:1910.08367] [INSPIRE].
[78] Henneaux, M.; Troessaert, C., Asymptotic symmetries of electromagnetism at spatial infinity, JHEP, 05, 137 (2018) · Zbl 1391.81129 · doi:10.1007/JHEP05(2018)137
[79] Maldacena, J.; Stanford, D.; Yang, Z., Diving into traversable wormholes, Fortsch. Phys., 65, 1700034 (2017) · doi:10.1002/prop.201700034
[80] L.V. Iliesiu, J. Kruthoff, G.J. Turiaci and H. Verlinde, JT gravity at finite cutoff, arXiv:2004.07242 [INSPIRE].
[81] D. Stanford and Z. Yang, Finite-cutoff JT gravity and self-avoiding loops, arXiv:2004.08005 [INSPIRE].
[82] A. Poole, K. Skenderis and M. Taylor, (A)dS_4in Bondi gauge, Class. Quant. Grav.36 (2019) 095005 [arXiv:1812.05369] [INSPIRE].
[83] Compère, G.; Fiorucci, A.; Ruzziconi, R., The Λ-BMS_4group of dS_4and new boundary conditions for AdS4, Class. Quant. Grav., 36, 195017 (2019) · Zbl 1478.83048 · doi:10.1088/1361-6382/ab3d4b
[84] Compère, G.; Fiorucci, A.; Ruzziconi, R., The Λ-BMS_4charge algebra, JHEP, 10, 205 (2020) · Zbl 1436.83005 · doi:10.1007/JHEP10(2020)205
[85] Afshar, HR, Warped Schwarzian theory, JHEP, 02, 126 (2020) · doi:10.1007/JHEP02(2020)126
[86] L.V. Iliesiu and G.J. Turiaci, The statistical mechanics of near-extremal black holes, arXiv:2003.02860 [INSPIRE].
[87] Polchinski, J.; Rosenhaus, V., The spectrum in the Sachdev-Ye-Kitaev model, JHEP, 04, 001 (2016) · Zbl 1388.81067 · doi:10.1007/JHEP04(2016)001
[88] Gaikwad, A.; Joshi, LK; Mandal, G.; Wadia, SR, Holographic dual to charged SYK from 3D gravity and Chern-Simons, JHEP, 02, 033 (2020) · Zbl 1435.83149 · doi:10.1007/JHEP02(2020)033
[89] A. Castro and W. Song, Comments on AdS_2gravity, arXiv:1411.1948 [INSPIRE].
[90] Mertens, TG; Turiaci, GJ; Verlinde, HL, Solving the Schwarzian via the conformal bootstrap, JHEP, 08, 136 (2017) · Zbl 1381.83089 · doi:10.1007/JHEP08(2017)136
[91] Bardeen, JM; Horowitz, GT, The extreme Kerr throat geometry: a vacuum analog of AdS_2 × S^2, Phys. Rev. D, 60, 104030 (1999) · doi:10.1103/PhysRevD.60.104030
[92] G. Sárosi, AdS_2holography and the SYK model, PoS(Modave2017)001 (2018) [arXiv:1711.08482] [INSPIRE].
[93] A.R. Brown, H. Gharibyan, H.W. Lin, L. Susskind, L. Thorlacius and Y. Zhao, Complexity of Jackiw-Teitelboim gravity, Phys. Rev. D99 (2019) 046016 [arXiv:1810.08741] [INSPIRE].
[94] Callan, CG Jr; Giddings, SB; Harvey, JA; Strominger, A., Evanescent black holes, Phys. Rev. D, 45, 1005 (1992) · doi:10.1103/PhysRevD.45.R1005
[95] Cangemi, D.; Jackiw, R., Gauge invariant formulations of lineal gravity, Phys. Rev. Lett., 69, 233 (1992) · Zbl 0968.81546 · doi:10.1103/PhysRevLett.69.233
[96] J. Maldacena and X.-L. Qi, Eternal traversable wormhole, arXiv:1804.00491 [INSPIRE].
[97] Hartman, T.; Strominger, A., Central charge for AdS_2quantum gravity, JHEP, 04, 026 (2009) · doi:10.1088/1126-6708/2009/04/026
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.