Abstract
The near horizon limit of the extremal BTZ black hole is a “self-dual orbifold” of AdS3. This geometry has a null circle on its boundary, and thus the dual field theory is a Discrete Light Cone Quantized (DLCQ) two dimensional CFT. The same geometry can be compactified to two dimensions giving AdS2 with a constant electric field. The kinematics of the DLCQ show that in a consistent quantum theory of gravity in these backgrounds there can be no dynamics in AdS2, which is consistent with older ideas about instabilities in this space. We show how the necessary boundary conditions eliminating AdS2 fluctuations can be implemented, leaving one copy of a Virasoro algebra as the asymptotic symmetry group. Our considerations clarify some aspects of the chiral CFTs appearing in proposed dual descriptions of the near-horizon degrees of freedom of extremal black holes.
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H.K. Kunduri, J. Lucietti and H.S. Reall, Near-horizon symmetries of extremal black holes, Class. Quant. Grav. 24 (2007) 4169 [arXiv:0705.4214] [SPIRES].
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [SPIRES].
O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large-N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183 [hep-th/9905111] [SPIRES].
M. Spradlin and A. Strominger, Vacuum states for AdS 2 black holes, JHEP 11 (1999) 021 [hep-th/9904143] [SPIRES].
D. Gaiotto et al., D4-D0 Branes on the Quintic, JHEP 03 (2006) 019 [hep-th/0509168] [SPIRES].
D. Gaiotto, A. Strominger and X. Yin, Superconformal black hole quantum mechanics, JHEP 11 (2005) 017 [hep-th/0412322] [SPIRES].
R.K. Gupta and A. Sen, AdS 3 /CFT 2 to AdS 2 /CFT 1, JHEP 04 (2009) 034 [arXiv:0806.0053] [SPIRES].
T. Azeyanagi, T. Nishioka and T. Takayanagi, Near Extremal Black Hole Entropy as Entanglement Entropy via AdS 2/CFT 1, Phys. Rev. D 77 (2008) 064005 [arXiv:0710.2956] [SPIRES].
A. Strominger, AdS 2 quantum gravity and string theory, JHEP 01 (1999) 007 [hep-th/9809027] [SPIRES].
V. Balasubramanian, A. Naqvi and J. Simon, A multi-boundary AdS orbifold and DLCQ holography: A universal holographic description of extremal black hole horizons, JHEP 08 (2004) 023 [hep-th/0311237] [SPIRES].
J.-H. Cho, T. Lee and G.W. Semenoff, Two dimensional anti-de Sitter space and discrete light cone quantization, Phys. Lett. B 468 (1999) 52 [hep-th/9906078] [SPIRES].
O. Coussaert and M. Henneaux, Self-dual solutions of 2+1 Einstein gravity with a negative cosmological constant, hep-th/9407181 [SPIRES].
J.D. Brown and M. Henneaux, Central Charges in the Canonical Realization of Asymptotic Symmetries: An Example from Three-Dimensional Gravity, Commun. Math. Phys. 104 (1986) 207 [SPIRES].
M. Guica, T. Hartman, W. Song and A. Strominger, The Kerr/CFT Correspondence, Phys. Rev. D 80 (2009) 124008 [arXiv:0809.4266] [SPIRES].
T. Hartman, K. Murata, T. Nishioka and A. Strominger, CFT Duals for Extreme Black Holes, JHEP 04 (2009) 019 [arXiv:0811.4393] [SPIRES].
J.M. Maldacena, J. Michelson and A. Strominger, Anti-de Sitter fragmentation, JHEP 02 (1999) 011 [hep-th/9812073] [SPIRES].
V. Balasubramanian, J. de Boer, V. Jejjala and J. Simon, Entropy of near-extremal black holes in AdS 5, JHEP 05 (2008) 067 [arXiv:0707.3601] [SPIRES].
R. Fareghbal, C.N. Gowdigere, A.E. Mosaffa and M.M. Sheikh-Jabbari, Nearing Extremal Intersecting Giants and New Decoupled Sectors in N = 4 SYM, JHEP 08 (2008) 070 [arXiv:0801.4457] [SPIRES].
R. Fareghbal, C.N. Gowdigere, A.E. Mosaffa and M.M. Sheikh-Jabbari, Nearing 1 1D Extremal Intersecting Giants and New Decoupled Sectors in D = 3, 6 SCFT’s, arXiv:0805.0203 [SPIRES].
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] [SPIRES].
O.J.C. Dias, H.S. Reall and J.E. Santos, Kerr-CFT and gravitational perturbations, JHEP 08 (2009) 101 [arXiv:0906.2380] [SPIRES].
M. Bañados, C. Teitelboim and J. Zanelli, The Black hole in three-dimensional space-time, Phys. Rev. Lett. 69 (1992) 1849 [hep-th/9204099] [SPIRES].
M. Bañados, M. Henneaux, C. Teitelboim and J. Zanelli, Geometry of the (2+1) black hole, Phys. Rev. D 48 (1993) 1506 [gr-qc/9302012] [SPIRES].
P. Kraus, Lectures on black holes and the AdS 3/CFT 2 correspondence, Lect. Notes Phys. 755 (2008) 193 [hep-th/0609074] [SPIRES].
J.R. David, G. Mandal and S.R. Wadia, Microscopic formulation of black holes in string theory, Phys. Rept. 369 (2002) 549 [hep-th/0203048] [SPIRES].
M. Bañados, M. Henneaux, C. Teitelboim and J. Zanelli, Geometry of the (2+1) black hole, Phys. Rev. D 48 (1993) 1506 [gr-qc/9302012] [SPIRES].
S. Carlip, Conformal field theory, (2+1)-dimensional gravity and the BTZ black hole, Class. Quant. Grav. 22 (2005) R85 [gr-qc/0503022] [SPIRES].
N. Seiberg, Why is the matrix model correct?, Phys. Rev. Lett. 79 (1997) 3577 [hep-th/9710009] [SPIRES].
A. Strominger and C. Vafa, Microscopic Origin of the Bekenstein-Hawking Entropy, Phys. Lett. B 379 (1996) 99 [hep-th/9601029] [SPIRES].
T. Hartman and A. Strominger, Central Charge for AdS 2 Quantum Gravity, JHEP 04 (2009) 026 [arXiv:0803.3621] [SPIRES].
A. Castro, D. Grumiller, F. Larsen and R. McNees, Holographic Description of AdS 2 Black Holes, JHEP 11 (2008) 052 [arXiv:0809.4264] [SPIRES].
D. Marolf and A. Yarom, Lodged in the throat: Internal infinities and AdS/CFT, JHEP 01 (2006) 141 [hep-th/0511225] [SPIRES].
B. Pioline and J. Troost, Schwinger pair production in AdS 2, JHEP 03 (2005) 043 [hep-th/0501169] [SPIRES].
J. Michelson and A. Strominger, Superconformal multi-black hole quantum mechanics, JHEP 09 (1999) 005 [hep-th/9908044] [SPIRES].
R. Dijkgraaf, R. Gopakumar, H. Ooguri and C. Vafa, Baby universes in string theory, Phys. Rev. D 73 (2006) 066002 [hep-th/0504221] [SPIRES].
J.M. Maldacena, Eternal black holes in Anti-de-Sitter, JHEP 04 (2003) 021 [hep-th/0106112] [SPIRES].
J.M. Bardeen and G.T. Horowitz, The extreme Kerr throat geometry: A vacuum analog of AdS 2 × S 2, Phys. Rev. D 60 (1999) 104030 [hep-th/9905099] [SPIRES].
H. Lü, J. Mei and C.N. Pope, Kerr/CFT Correspondence in Diverse Dimensions, JHEP 04 (2009) 054 [arXiv:0811.2225] [SPIRES].
D.D.K. Chow, M. Cvetič, H. Lü and C.N. Pope, Extremal Black Hole/CFT Correspondence in (Gauged) Supergravities, Phys. Rev. D 79 (2009) 084018 [arXiv:0812.2918] [SPIRES].
T. Azeyanagi, N. Ogawa and S. Terashima, Holographic Duals of Kaluza-Klein Black Holes, JHEP 04 (2009) 061 [arXiv:0811.4177] [SPIRES].
H. Isono, T.-S. Tai and W.-Y. Wen, Kerr/CFT correspondence and five-dimensional BMPV black holes, Int. J. Mod. Phys. A 24 (2009) 5659 [arXiv:0812.4440] [SPIRES].
C.-M. Chen and J.E. Wang, Holographic Duals of Black Holes in Five-dimensional Minimal Supergravity, arXiv:0901.0538 [SPIRES].
F. Loran and H. Soltanpanahi, Near the horizon of 5D black rings, JHEP 03 (2009) 035 [arXiv:0810.2620] [SPIRES].
F. Loran and H. Soltanpanahi, 5D Extremal Rotating Black Holes and CFT duals, Class. Quant. Grav. 26 (2009) 155019 [arXiv:0901.1595] [SPIRES].
H. Lü, J.-w. Mei, C.N. Pope and J.F. Vazquez-Poritz, Extremal Static AdS Black Hole/CFT Correspondence in Gauged Supergravities, Phys. Lett. B 673 (2009) 77 [arXiv:0901.1677] [SPIRES].
G. Compere, K. Murata and T. Nishioka, Central Charges in Extreme Black Hole/CFT Correspondence, JHEP 05 (2009) 077 [arXiv:0902.1001] [SPIRES].
T. Azeyanagi, N. Ogawa and S. Terashima, The Kerr/CFT Correspondence and String Theory, Phys. Rev. D 79 (2009) 106009 [arXiv:0812.4883] [SPIRES].
A.N. Schellekens and N.P. Warner, Anomalies and modular invariance in string theory, Phys. Lett. B 177 (1986) 317 [SPIRES].
E. Witten, Elliptic genera and quantum field theory, Commun. Math. Phys. 109 (1987) 525 [SPIRES].
J. Maldacena, D. Martelli and Y. Tachikawa, Comments on string theory backgrounds with non- relativistic conformal symmetry, JHEP 10 (2008) 072 [arXiv:0807.1100] [SPIRES].
K. Balasubramanian and J. McGreevy, Gravity duals for non-relativistic CFTs, Phys. Rev. Lett. 101 (2008) 061601 [arXiv:0804.4053] [SPIRES].
C.P. Herzog, M. Rangamani and S.F. Ross, Heating up Galilean holography, JHEP 11 (2008) 080 [arXiv:0807.1099] [SPIRES].
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ArXiv ePrint: 0906.3272
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Balasubramanian, V., de Boer, J., Sheikh-Jabbari, M. et al. What is a chiral 2d CFT? And what does it have to do with extremal black holes?. J. High Energ. Phys. 2010, 17 (2010). https://doi.org/10.1007/JHEP02(2010)017
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DOI: https://doi.org/10.1007/JHEP02(2010)017