Abstract
It has been argued recently by Almheiri and Polchinski that the near-horizon conformal symmetry of extremal black holes must be broken due to gravitational backreaction at an IR scale linear in G N . In this paper, we show that this scale coincides with the so-called ‘thermodynamic mass gap’ of near-extremal black holes, a scale which signals the breakdown of their thermodynamic description. We also develop a method which extends the analysis of Almheiri and Polchinski to more complicated models with extremal throats by studying the bulk linearized quantum field theory. Moreover, we show how their original model correctly captures the universal physics of the near-horizon region of near-extremal black holes at tree level, and conclude that this equivalence of the conformal breaking and mass gap scale is general.
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References
A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett. B 379 (1996) 99 [hep-th/9601029] [INSPIRE].
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
K. Jensen, S. Kachru, A. Karch, J. Polchinski and E. Silverstein, Towards a holographic marginal Fermi liquid, Phys. Rev. D 84 (2011) 126002 [arXiv:1105.1772] [INSPIRE].
J.M. Maldacena, J. Michelson and A. Strominger, Anti-de Sitter fragmentation, JHEP 02 (1999) 011 [hep-th/9812073] [INSPIRE].
A. Almheiri and J. Polchinski, Models of AdS 2 backreaction and holography, JHEP 11 (2015) 014 [arXiv:1402.6334] [INSPIRE].
R. Jackiw, Lower dimensional gravity, Nucl. Phys. B 252 (1985) 343 [INSPIRE].
C. Teitelboim, Gravitation and Hamiltonian structure in two space-time dimensions, Phys. Lett. B 126 (1983) 41 [INSPIRE].
J. Preskill, P. Schwarz, A.D. Shapere, S. Trivedi and F. Wilczek, Limitations on the statistical description of black holes, Mod. Phys. Lett. A 6 (1991) 2353 [INSPIRE].
J.M. Maldacena and L. Susskind, D-branes and fat black holes, Nucl. Phys. B 475 (1996) 679 [hep-th/9604042] [INSPIRE].
J.M. Maldacena and A. Strominger, Universal low-energy dynamics for rotating black holes, Phys. Rev. D 56 (1997) 4975 [hep-th/9702015] [INSPIRE].
K. Jensen, Chaos in AdS 2 holography, Phys. Rev. Lett. 117 (2016) 111601 [arXiv:1605.06098] [INSPIRE].
J. Maldacena, D. Stanford and Z. Yang, Conformal symmetry and its breaking in two dimensional nearly anti-de-Sitter space, arXiv:1606.01857 [INSPIRE].
J. Engelsöy, T.G. Mertens and H. Verlinde, An investigation of AdS 2 backreaction and holography, JHEP 07 (2016) 139 [arXiv:1606.03438] [INSPIRE].
D.N. Page, Thermodynamics of near extreme black holes, hep-th/0012020 [INSPIRE].
G. ’t Hooft, Dimensional reduction in quantum gravity, in Salamfest, (1993) [gr-qc/9310026] [INSPIRE].
L. Susskind, The world as a hologram, J. Math. Phys. 36 (1995) 6377 [hep-th/9409089] [INSPIRE].
M. Bañados, C. Teitelboim and J. Zanelli, The black hole in three-dimensional space-time, Phys. Rev. Lett. 69 (1992) 1849 [hep-th/9204099] [INSPIRE].
A. Strominger, AdS 2 quantum gravity and string theory, JHEP 01 (1999) 007 [hep-th/9809027] [INSPIRE].
A. Castro, D. Grumiller, F. Larsen and R. McNees, Holographic description of AdS 2 black holes, JHEP 11 (2008) 052 [arXiv:0809.4264] [INSPIRE].
E. Keski-Vakkuri, Bulk and boundary dynamics in BTZ black holes, Phys. Rev. D 59 (1999) 104001 [hep-th/9808037] [INSPIRE].
A. Chamblin, R. Emparan, C.V. Johnson and R.C. Myers, Charged AdS black holes and catastrophic holography, Phys. Rev. D 60 (1999) 064018 [hep-th/9902170] [INSPIRE].
T. Faulkner, H. Liu, J. McGreevy and D. Vegh, Emergent quantum criticality, Fermi surfaces and AdS 2, Phys. Rev. D 83 (2011) 125002 [arXiv:0907.2694] [INSPIRE].
A. Almheiri and B. Kang, work in progress.
M. Cadoni and S. Mignemi, Asymptotic symmetries of AdS 2 and conformal group in D = 1, Nucl. Phys. B 557 (1999) 165 [hep-th/9902040] [INSPIRE].
D. Grumiller, J. Salzer and D. Vassilevich, AdS 2 holography is (non-)trivial for (non-)constant dilaton, JHEP 12 (2015) 015 [arXiv:1509.08486] [INSPIRE].
A. Castro and F. Larsen, Near extremal Kerr entropy from AdS 2 quantum gravity, JHEP 12 (2009) 037 [arXiv:0908.1121] [INSPIRE].
M. Guica, T. Hartman, W. Song and A. Strominger, The Kerr/CFT correspondence, Phys. Rev. D 80 (2009) 124008 [arXiv:0809.4266] [INSPIRE].
A.J. Amsel, G.T. Horowitz, D. Marolf and M.M. Roberts, No dynamics in the extremal Kerr throat, JHEP 09 (2009) 044 [arXiv:0906.2376] [INSPIRE].
S.D. Mathur, The information paradox: a pedagogical introduction, Class. Quant. Grav. 26 (2009) 224001 [arXiv:0909.1038] [INSPIRE].
T. Hartman and A. Strominger, Central charge for AdS 2 quantum gravity, JHEP 04 (2009) 026 [arXiv:0803.3621] [INSPIRE].
M. Taylor, Lifshitz holography, Class. Quant. Grav. 33 (2016) 033001 [arXiv:1512.03554] [INSPIRE].
J. Tarrio and S. Vandoren, Black holes and black branes in Lifshitz spacetimes, JHEP 09 (2011) 017 [arXiv:1105.6335] [INSPIRE].
M. Alishahiha, E. O Colgain and H. Yavartanoo, Charged black branes with hyperscaling violating factor, JHEP 11 (2012) 137 [arXiv:1209.3946] [INSPIRE].
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ArXiv ePrint: 1606.04108
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Almheiri, A., Kang, B. Conformal symmetry breaking and thermodynamics of near-extremal black holes. J. High Energ. Phys. 2016, 52 (2016). https://doi.org/10.1007/JHEP10(2016)052
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DOI: https://doi.org/10.1007/JHEP10(2016)052