Abstract
Black holes have an enormous underlying space of microstates, but universal macroscopic physics characterized by mass, charge and angular momentum as well as a causally disconnected interior. This leads to two related puzzles: (1) How does the effective factorization of interior and exterior degrees of freedom emerge in gravity?, and (2) How does the underlying degeneracy of states wind up having a geometric realization in the horizon area and in properties of the singularity? We explore these puzzles in the context of an incipient black hole in the AdS/CFT correspondence, the microstates of which are dual to half-BPS states of the \( \mathcal{N} \) = 4 super-Yang-Mills theory. First, we construct a code subspace for this black hole and show how to organize it as a tensor product of a universal macroscopic piece (describing the exterior), and a factor corresponding to the microscopic degrees of freedom (describing the interior). We then study the classical phase space and symplectic form for low-energy excitations around the black hole. On the AdS side, we find that the symplectic form has a new physical degree of freedom at the stretched horizon of the black hole, reminiscent of soft hair, which is absent in the microstates. We explicitly show how such a soft mode emerges from the microscopic phase space in the dual CFT via a canonical transformation and how it encodes partial information about the microscopic degrees of freedom of the black hole.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
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].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
V. Balasubramanian, J. de Boer, V. Jejjala and J. Simon, The library of Babel: on the origin of gravitational thermodynamics, JHEP 12 (2005) 006 [hep-th/0508023] [INSPIRE].
R.C. Myers and O. Tafjord, Superstars and giant gravitons, JHEP 11 (2001) 009 [hep-th/0109127] [INSPIRE].
O. Lunin and S.D. Mathur, AdS/CFT duality and the black hole information paradox, Nucl. Phys. B 623 (2002) 342 [hep-th/0109154] [INSPIRE].
O. Lunin and S.D. Mathur, Statistical interpretation of Bekenstein entropy for systems with a stretched horizon, Phys. Rev. Lett. 88 (2002) 211303 [hep-th/0202072] [INSPIRE].
S.D. Mathur, The fuzzball proposal for black holes: an elementary review, Fortsch. Phys. 53 (2005) 793 [hep-th/0502050] [INSPIRE].
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] [INSPIRE].
A. Almheiri, X. Dong and D. Harlow, Bulk locality and quantum error correction in AdS/CFT, JHEP 04 (2015) 163 [arXiv:1411.7041] [INSPIRE].
K. Papadodimas and S. Raju, An Infalling Observer in AdS/CFT, JHEP 10 (2013) 212 [arXiv:1211.6767] [INSPIRE].
L. Grant et al., Minisuperspace quantization of ‘bubbling AdS’ and free fermion droplets, JHEP 08 (2005) 025 [hep-th/0505079] [INSPIRE].
L. Maoz and V.S. Rychkov, Geometry quantization from supergravity: The Case of ‘bubbling AdS’, JHEP 08 (2005) 096 [hep-th/0508059] [INSPIRE].
P.V. Buividovich and M.I. Polikarpov, Entanglement entropy in gauge theories and the holographic principle for electric strings, Phys. Lett. B 670 (2008) 141 [arXiv:0806.3376] [INSPIRE].
S. Ghosh, R.M. Soni and S.P. Trivedi, On the entanglement entropy for gauge theories, JHEP 09 (2015) 069 [arXiv:1501.02593] [INSPIRE].
W. Donnelly and A.C. Wall, Geometric entropy and edge modes of the electromagnetic field, Phys. Rev. D 94 (2016) 104053 [arXiv:1506.05792] [INSPIRE].
W. Donnelly and L. Freidel, Local subsystems in gauge theory and gravity, JHEP 09 (2016) 102 [arXiv:1601.04744] [INSPIRE].
J.R. Fliss et al., Interface contributions to topological entanglement in abelian Chern-Simons theory, JHEP 09 (2017) 056 [arXiv:1705.09611] [INSPIRE].
D. Harlow, The Ryu–Takayanagi formula from quantum error correction, Commun. Math. Phys. 354 (2017) 865 [arXiv:1607.03901] [INSPIRE].
J. Lin, Ryu-Takayanagi area as an entanglement edge term, arXiv:1704.07763 [INSPIRE].
J. Lin, Entanglement entropy in Jackiw-Teitelboim gravity, arXiv:1807.06575 [INSPIRE].
S.W. Hawking, M.J. Perry and A. Strominger, Soft hair on black holes, Phys. Rev. Lett. 116 (2016) 231301 [arXiv:1601.00921] [INSPIRE].
L. Donnay, G. Giribet, H.A. Gonzalez and M. Pino, Supertranslations and superrotations at the black hole horizon, Phys. Rev. Lett. 116 (2016) 091101 [arXiv:1511.08687] [INSPIRE].
L. Donnay, G. Giribet, H.A. González and M. Pino, Extended symmetries at the black hole horizon, JHEP 09 (2016) 100 [arXiv:1607.05703] [INSPIRE].
L. Donnay, G. Giribet, H.A. González and A. Puhm, Black hole memory effect, Phys. Rev. D 98 (2018) 124016 [arXiv:1809.07266] [INSPIRE].
S. Haco, S.W. Hawking, M.J. Perry and A. Strominger, Black hole entropy and soft hair, JHEP 12 (2018) 098 [arXiv:1810.01847] [INSPIRE].
D. Berenstein, A toy model for the AdS/CFT correspondence, JHEP 07 (2004) 018 [hep-th/0403110] [INSPIRE].
S. Corley, A. Jevicki and S. Ramgoolam, Exact correlators of giant gravitons from dual N = 4 SYM theory, Adv. Theor. Math. Phys. 5 (2002) 809 [hep-th/0111222] [INSPIRE].
S. Lee, S. Minwalla, M. Rangamani and N. Seiberg, Three point functions of chiral operators in D = 4, N = 4 SYM at large N, Adv. Theor. Math. Phys. 2 (1998) 697 [hep-th/9806074] [INSPIRE].
A. Ghodsi, A.E. Mosaffa, O. Saremi and M.M. Sheikh-Jabbari, LLL vs. LLM: half BPS sector of N = 4 SYM equals to quantum Hall system, Nucl. Phys. B 729 (2005) 467 [hep-th/0505129] [INSPIRE].
D. Berenstein and A. Miller, Superposition induced topology changes in quantum gravity, JHEP 11 (2017) 121 [arXiv:1702.03011] [INSPIRE].
D. Berenstein and A. Miller, Code subspaces for LLM geometries, Class. Quant. Grav. 35 (2018) 065003 [arXiv:1708.00035] [INSPIRE].
A. Dhar, G. Mandal and S.R. Wadia, Classical Fermi fluid and geometric action for c = 1, Int. J. Mod. Phys. A 8 (1993) 325 [hep-th/9204028] [INSPIRE].
A. Dhar, Two-dimensional string theory from the c = 1 matrix model, Nucl. Phys. Proc. Suppl. B 45 (1996) 234.
A. Dhar, G. Mandal and S.R. Wadia, W(∞) coherent states and path integral derivation of bosonization of nonrelativistic fermions in one-dimension, Mod. Phys. Lett. A 8 (1993) 3557 [hep-th/9309028] [INSPIRE].
V. Balasubramanian et al., Quantum geometry and gravitational entropy, JHEP 12 (2007) 067 [arXiv:0705.4431] [INSPIRE].
N.V. Suryanarayana, Half-BPS giants, free fermions and microstates of superstars, JHEP 01 (2006) 082 [hep-th/0411145] [INSPIRE].
J. Simon, Correlations vs connectivity in R-charge, JHEP 10 (2018) 048 [arXiv:1805.11279] [INSPIRE].
J. McGreevy, L. Susskind and N. Toumbas, Invasion of the giant gravitons from Anti-de Sitter space, JHEP 06 (2000) 008 [hep-th/0003075] [INSPIRE].
V. Balasubramanian, M. Berkooz, A. Naqvi and M.J. Strassler, Giant gravitons in conformal field theory, JHEP 04 (2002) 034 [hep-th/0107119] [INSPIRE].
V. Balasubramanian, B. Czech, K. Larjo and J. Simon, Integrability versus information loss: a simple example, JHEP 11 (2006) 001 [hep-th/0602263] [INSPIRE].
J.M. Deutsch, Quantum statistical mechanics in a closed system, Phys. Rev. A 43 (1991) 2046.
M. Srednicki, Chaos and quantum thermalization, Phys. Rev. E 50 (1994) 888.
N. Lashkari, A. Dymarsky and H. Liu, Eigenstate thermalization hypothesis in conformal field theory, J. Stat. Mech. 1803 (2018) 033101 [arXiv:1610.00302] [INSPIRE].
V. Balasubramanian et al., Typicality versus thermality: an analytic distinction, Gen. Rel. Grav. 40 (2008) 1863 [hep-th/0701122] [INSPIRE].
P. Hayden and G. Penington, Learning the alpha-bits of black holes, arXiv:1807.06041 [INSPIRE].
T. Faulkner and H. Wang, Probing beyond ETH at large c, JHEP 06 (2018) 123 [arXiv:1712.03464] [INSPIRE].
V. Balasubramanian et al., Emergent classical spacetime from microstates of an incipient black hole II, work in progress.
K. Papadodimas and S. Raju, Black hole interior in the holographic correspondence and the information paradox, Phys. Rev. Lett. 112 (2014) 051301 [arXiv:1310.6334] [INSPIRE].
H. Lin, O. Lunin and J.M. Maldacena, Bubbling AdS space and 1/2 BPS geometries, JHEP 10 (2004) 025 [hep-th/0409174] [INSPIRE].
A.E. Mosaffa and M.M. Sheikh-Jabbari, On classification of the bubbling geometries, JHEP 04 (2006) 045 [hep-th/0602270] [INSPIRE].
K. Skenderis and M. Taylor, Anatomy of bubbling solutions, JHEP 09 (2007) 019 [arXiv:0706.0216] [INSPIRE].
L.G. Yaffe, Large N limits as classical mechanics, Rev. Mod. Phys. 54 (1982) 407 [INSPIRE].
E. Witten, Coadjoint orbits of the Virasoro group, Commun. Math. Phys. 114 (1988) 1 [INSPIRE].
A. Belin, A. Lewkowycz and G. Sárosi, The boundary dual of the bulk symplectic form, Phys. Lett. B 789 (2019) 71 [arXiv:1806.10144] [INSPIRE].
A. Caldeira and A. Leggett, Path integral approach to quantum brownian motion, Physica A 121 (1983) 587.
C. Agon, V. Balasubramanian, S. Kasko and A. Lawrence, Coarse grained quantum dynamics, Phys. Rev. D 98 (2018) 025019 [arXiv:1412.3148] [INSPIRE].
V. Balasubramanian, J. de Boer, S. El-Showk and I. Messamah, Black holes as effective geometries, Class. Quant. Grav. 25 (2008) 214004 [arXiv:0811.0263] [INSPIRE].
A. Dhar, G. Mandal and N.V. Suryanarayana, Exact operator bosonization of finite number of fermions in one space dimension, JHEP 01 (2006) 118 [hep-th/0509164] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1810.13440
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Balasubramanian, V., Berenstein, D., Lewkowycz, A. et al. Emergent classical spacetime from microstates of an incipient black hole. J. High Energ. Phys. 2019, 197 (2019). https://doi.org/10.1007/JHEP01(2019)197
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2019)197