Abstract
We study information theoretic properties of planar black hole microstates in 2 + 1 dimensional asymptotically anti-de Sitter spacetime, modeled by black holes with an end-of-the-world brane behind the horizon. The von Neumann entropy of sufficiently large subregions in the dual CFT exhibits a time-dependent phase, which from a doubly-holographic perspective corresponds to the appearance of quantum extremal islands in the brane description. Considering the case where dilaton gravity is added to the brane, we show that tuning the associated couplings affects the propagation of information in the dual CFT state. By requiring that information theoretic bounds on the growth of entanglement entropy are satisfied in the dual CFT, we can place bounds on the allowed values of the couplings on the brane. Furthermore, we initiate the study of brane tomography, by showing how subleading corrections to the entanglement velocity can be used to learn about the properties of the brane as well as any gravitational dynamics localized on it.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
G. ‘t Hooft, Dimensional reduction in quantum gravity, Conf. Proc. C 930308 (1993) 284 [gr-qc/9310026] [INSPIRE].
L. Susskind, The World as a hologram, J. Math. Phys. 36 (1995) 6377 [hep-th/9409089] [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].
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].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
T. Hartman and J. Maldacena, Time Evolution of Entanglement Entropy from Black Hole Interiors, JHEP 05 (2013) 014 [arXiv:1303.1080] [INSPIRE].
T. Takayanagi, Holographic Dual of BCFT, Phys. Rev. Lett. 107 (2011) 101602 [arXiv:1105.5165] [INSPIRE].
M. Fujita, T. Takayanagi and E. Tonni, Aspects of AdS/BCFT, JHEP 11 (2011) 043 [arXiv:1108.5152] [INSPIRE].
I. Kourkoulou and J. Maldacena, Pure states in the SYK model and nearly-AdS2 gravity, arXiv:1707.02325 [INSPIRE].
A. Almheiri, A. Mousatov and M. Shyani, Escaping the Interiors of Pure Boundary-State Black Holes, arXiv:1803.04434 [INSPIRE].
S. Cooper, M. Rozali, B. Swingle, M. Van Raamsdonk, C. Waddell and D. Wakeham, Black hole microstate cosmology, JHEP 07 (2019) 065 [arXiv:1810.10601] [INSPIRE].
M. Miyaji, T. Takayanagi and T. Ugajin, Spectrum of End of the World Branes in Holographic BCFTs, JHEP 06 (2021) 023 [arXiv:2103.06893] [INSPIRE].
J. Chandra and T. Hartman, Coarse graining pure states in AdS/CFT, arXiv:2206.03414 [INSPIRE].
S. Antonini and B. Swingle, Cosmology at the end of the world, Nature Phys. 16 (2020) 881 [arXiv:1907.06667] [INSPIRE].
Y. Chen, V. Gorbenko and J. Maldacena, Bra-ket wormholes in gravitationally prepared states, JHEP 02 (2021) 009 [arXiv:2007.16091] [INSPIRE].
M. Van Raamsdonk, Comments on wormholes, ensembles, and cosmology, JHEP 12 (2021) 156 [arXiv:2008.02259] [INSPIRE].
Z. Wang, Z. Xu, S. Zhou and Y. Zhou, Partial reduction and cosmology at defect brane, JHEP 05 (2022) 049 [arXiv:2112.13782] [INSPIRE].
S. Fallows and S.F. Ross, Constraints on cosmologies inside black holes, JHEP 05 (2022) 094 [arXiv:2203.02523] [INSPIRE].
C. Waddell, Bottom-up holographic models for cosmology, JHEP 09 (2022) 176 [arXiv:2203.03096] [INSPIRE].
S. Antonini, P. Simidzija, B. Swingle and M. Van Raamsdonk, Cosmology from the vacuum, arXiv:2203.11220 [INSPIRE].
L. Randall and R. Sundrum, An Alternative to compactification, Phys. Rev. Lett. 83 (1999) 4690 [hep-th/9906064] [INSPIRE].
A. Karch and L. Randall, Locally localized gravity, JHEP 05 (2001) 008 [hep-th/0011156] [INSPIRE].
T. Azeyanagi, A. Karch, T. Takayanagi and E.G. Thompson, Holographic calculation of boundary entropy, JHEP 03 (2008) 054 [arXiv:0712.1850] [INSPIRE].
S. Cooper, D. Neuenfeld, M. Rozali and D. Wakeham, Brane dynamics from the first law of entanglement, JHEP 03 (2020) 023 [arXiv:1912.05746] [INSPIRE].
W. Reeves, M. Rozali, P. Simidzija, J. Sully, C. Waddell and D. Wakeham, Looking for (and not finding) a bulk brane, JHEP 12 (2021) 002 [arXiv:2108.10345] [INSPIRE].
A. Belin, S. Biswas and J. Sully, The spectrum of boundary states in symmetric orbifolds, JHEP 01 (2022) 123 [arXiv:2110.05491] [INSPIRE].
Y. Kusuki, Analytic bootstrap in 2D boundary conformal field theory: towards braneworld holography, JHEP 03 (2022) 161 [arXiv:2112.10984] [INSPIRE].
T. Kawamoto, T. Mori, Y.-k. Suzuki, T. Takayanagi and T. Ugajin, Holographic local operator quenches in BCFTs, JHEP 05 (2022) 060 [arXiv:2203.03851] [INSPIRE].
K. Izumi, T. Shiromizu, K. Suzuki, T. Takayanagi and N. Tanahashi, Brane dynamics of holographic BCFTs, JHEP 10 (2022) 050 [arXiv:2205.15500] [INSPIRE].
T. Anous, M. Meineri, P. Pelliconi and J. Sonner, Sailing past the End of the World and discovering the Island, SciPost Phys. 13 (2022) 075 [arXiv:2202.11718] [INSPIRE].
A. Almheiri, R. Mahajan, J. Maldacena and Y. Zhao, The Page curve of Hawking radiation from semiclassical geometry, JHEP 03 (2020) 149 [arXiv:1908.10996] [INSPIRE].
M. Rozali, J. Sully, M. Van Raamsdonk, C. Waddell and D. Wakeham, Information radiation in BCFT models of black holes, JHEP 05 (2020) 004 [arXiv:1910.12836] [INSPIRE].
A. Almheiri, R. Mahajan and J.E. Santos, Entanglement islands in higher dimensions, SciPost Phys. 9 (2020) 001 [arXiv:1911.09666] [INSPIRE].
V. Balasubramanian, A. Kar, O. Parrikar, G. Sárosi and T. Ugajin, Geometric secret sharing in a model of Hawking radiation, JHEP 01 (2021) 177 [arXiv:2003.05448] [INSPIRE].
J. Sully, M.V. Raamsdonk and D. Wakeham, BCFT entanglement entropy at large central charge and the black hole interior, JHEP 03 (2021) 167 [arXiv:2004.13088] [INSPIRE].
H. Geng and A. Karch, Massive islands, JHEP 09 (2020) 121 [arXiv:2006.02438] [INSPIRE].
H.Z. Chen, R.C. Myers, D. Neuenfeld, I.A. Reyes and J. Sandor, Quantum Extremal Islands Made Easy, Part I: Entanglement on the Brane, JHEP 10 (2020) 166 [arXiv:2006.04851] [INSPIRE].
H.Z. Chen, R.C. Myers, D. Neuenfeld, I.A. Reyes and J. Sandor, Quantum Extremal Islands Made Easy, Part II: Black Holes on the Brane, JHEP 12 (2020) 025 [arXiv:2010.00018] [INSPIRE].
G. Grimaldi, J. Hernandez and R.C. Myers, Quantum extremal islands made easy. Part IV. Massive black holes on the brane, JHEP 03 (2022) 136 [arXiv:2202.00679] [INSPIRE].
C. Krishnan, Critical Islands, JHEP 01 (2021) 179 [arXiv:2007.06551] [INSPIRE].
F. Deng, J. Chu and Y. Zhou, Defect extremal surface as the holographic counterpart of Island formula, JHEP 03 (2021) 008 [arXiv:2012.07612] [INSPIRE].
A. May and D. Wakeham, Quantum tasks require islands on the brane, Class. Quant. Grav. 38 (2021) 144001 [arXiv:2102.01810] [INSPIRE].
S. Fallows and S.F. Ross, Islands and mixed states in closed universes, JHEP 07 (2021) 022 [arXiv:2103.14364] [INSPIRE].
D. Neuenfeld, The Dictionary for Double Holography and Graviton Masses in d Dimensions, arXiv:2104.02801 [INSPIRE].
H. Geng, S. Lüst, R.K. Mishra and D. Wakeham, Holographic BCFTs and Communicating Black Holes, jhep 08 (2021) 003 [arXiv:2104.07039] [INSPIRE].
J. Chu, F. Deng and Y. Zhou, Page curve from defect extremal surface and island in higher dimensions, JHEP 10 (2021) 149 [arXiv:2105.09106] [INSPIRE].
M. Miyaji, Island for gravitationally prepared state and pseudo entanglement wedge, JHEP 12 (2021) 013 [arXiv:2109.03830] [INSPIRE].
E. Verheijden and E. Verlinde, From the BTZ black hole to JT gravity: geometrizing the island, JHEP 11 (2021) 092 [arXiv:2102.00922] [INSPIRE].
H. Geng, A. Karch, C. Perez-Pardavila, S. Raju, L. Randall, M. Riojas et al., Entanglement phase structure of a holographic BCFT in a black hole background, JHEP 05 (2022) 153 [arXiv:2112.09132] [INSPIRE].
K. Suzuki and T. Takayanagi, BCFT and Islands in two dimensions, JHEP 06 (2022) 095 [arXiv:2202.08462] [INSPIRE].
L. Bianchi, S. De Angelis and M. Meineri, Radiation, entanglement and islands from a boundary local quench, arXiv:2203.10103 [INSPIRE].
H. Geng, A. Karch, C. Perez-Pardavila, S. Raju, L. Randall, M. Riojas et al., Jackiw-Teitelboim Gravity from the Karch-Randall Braneworld, arXiv:2206.04695 [INSPIRE].
S. Chapman, D. Ge and G. Policastro, Holographic Complexity for Defects Distinguishes Action from Volume, JHEP 05 (2019) 049 [arXiv:1811.12549] [INSPIRE].
S.F. Ross, Complexity and typical microstates, Phys. Rev. D 100 (2019) 066014 [arXiv:1905.06211] [INSPIRE].
Y. Sato and K. Watanabe, Does Boundary Distinguish Complexities?, JHEP 11 (2019) 132 [arXiv:1908.11094] [INSPIRE].
P. Braccia, A.L. Cotrone and E. Tonni, Complexity in the presence of a boundary, JHEP 02 (2020) 051 [arXiv:1910.03489] [INSPIRE].
J. Hernandez, R.C. Myers and S.-M. Ruan, Quantum extremal islands made easy. Part III. Complexity on the brane, JHEP 02 (2021) 173 [arXiv:2010.16398] [INSPIRE].
F. Omidi, Regularizations of Action-Complexity for a Pure BTZ Black Hole Microstate, JHEP 07 (2020) 020 [arXiv:2004.11628] [INSPIRE].
A. Bhattacharya, A. Bhattacharyya, P. Nandy and A.K. Patra, Islands and complexity of eternal black hole and radiation subsystems for a doubly holographic model, JHEP 05 (2021) 135 [arXiv:2103.15852] [INSPIRE].
R. Auzzi, S. Baiguera, S. Bonansea and G. Nardelli, Action complexity in the presence of defects and boundaries, JHEP 02 (2022) 118 [arXiv:2112.03290] [INSPIRE].
E. D’Hoker, J. Estes and M. Gutperle, Exact half-BPS Type IIB interface solutions. I. Local solution and supersymmetric Janus, JHEP 06 (2007) 021 [arXiv:0705.0022] [INSPIRE].
E. D’Hoker, J. Estes and M. Gutperle, Exact half-BPS Type IIB interface solutions. II. Flux solutions and multi-Janus, JHEP 06 (2007) 022 [arXiv:0705.0024] [INSPIRE].
M. Chiodaroli, E. D’Hoker and M. Gutperle, Holographic duals of Boundary CFTs, JHEP 07 (2012) 177 [arXiv:1205.5303] [INSPIRE].
D. Bak, C. Kim, S.-H. Yi and J. Yoon, Unitarity of entanglement and islands in two-sided Janus black holes, JHEP 01 (2021) 155 [arXiv:2006.11717] [INSPIRE].
C.F. Uhlemann, Islands and Page curves in 4d from Type IIB, JHEP 08 (2021) 104 [arXiv:2105.00008] [INSPIRE].
M. Van Raamsdonk and C. Waddell, Finding AdS5 × S5 in 2 + 1 dimensional SCFT physics, JHEP 11 (2021) 145 [arXiv:2109.04479] [INSPIRE].
G.R. Dvali, G. Gabadadze and M. Porrati, 4-D gravity on a brane in 5-D Minkowski space, Phys. Lett. B 485 (2000) 208 [hep-th/0005016] [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].
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
S. Ryu and T. Takayanagi, Aspects of Holographic Entanglement Entropy, JHEP 08 (2006) 045 [hep-th/0605073] [INSPIRE].
V.E. Hubeny, M. Rangamani and T. Takayanagi, A Covariant holographic entanglement entropy proposal, JHEP 07 (2007) 062 [arXiv:0705.0016] [INSPIRE].
M. Rangamani and T. Takayanagi, Holographic Entanglement Entropy, Lecture Notes in Physics 931, Springer (2017) [DOI] [arXiv:1609.01287] [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].
H. Liu and S.J. Suh, Entanglement Tsunami: Universal Scaling in Holographic Thermalization, Phys. Rev. Lett. 112 (2014) 011601 [arXiv:1305.7244] [INSPIRE].
H. Liu and S.J. Suh, Entanglement growth during thermalization in holographic systems, Phys. Rev. D 89 (2014) 066012 [arXiv:1311.1200] [INSPIRE].
T. Hartman and N. Afkhami-Jeddi, Speed Limits for Entanglement, arXiv:1512.02695 [INSPIRE].
S. de Haro, S.N. Solodukhin and K. Skenderis, Holographic reconstruction of space-time and renormalization in the AdS/CFT correspondence, Commun. Math. Phys. 217 (2001) 595 [hep-th/0002230] [INSPIRE].
J.M. Maldacena, Eternal black holes in anti-de Sitter, JHEP 04 (2003) 021 [hep-th/0106112] [INSPIRE].
S.S. Gubser, AdS/CFT and gravity, Phys. Rev. D 63 (2001) 084017 [hep-th/9912001] [INSPIRE].
T. Nishioka, S. Ryu and T. Takayanagi, Holographic Entanglement Entropy: An Overview, J. Phys. A 42 (2009) 504008 [arXiv:0905.0932] [INSPIRE].
T. Kibe, P. Mandayam and A. Mukhopadhyay, Holographic spacetime, black holes and quantum error correcting codes: a review, Eur. Phys. J. C 82 (2022) 463 [arXiv:2110.14669] [INSPIRE].
J. Cardy and E. Tonni, Entanglement hamiltonians in two-dimensional conformal field theory, J. Stat. Mech. 1612 (2016) 123103 [arXiv:1608.01283] [INSPIRE].
T. Grover, Certain general constraints on the many-body localization transition, arXiv:1405.1471.
V. Balasubramanian and P. Kraus, A Stress tensor for Anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [INSPIRE].
D. Grumiller, R. Ruzziconi and C. Zwikel, Generalized dilaton gravity in 2d, SciPost Phys. 12 (2022) 032 [arXiv:2109.03266] [INSPIRE].
M. Mezei and J. Virrueta, The Quantum Null Energy Condition and Entanglement Entropy in Quenches, arXiv:1909.00919 [INSPIRE].
U. Moitra, S.K. Sake, S.P. Trivedi and V. Vishal, Jackiw-Teitelboim Model Coupled to Conformal Matter in the Semi-Classical Limit, JHEP 04 (2020) 199 [arXiv:1908.08523] [INSPIRE].
T. Banks, P. Draper and B. Zhang, JT Gravity Coupled to Fermions, arXiv:2205.07382 [INSPIRE].
T. Hartman, Y. Jiang and E. Shaghoulian, Islands in cosmology, JHEP 11 (2020) 111 [arXiv:2008.01022] [INSPIRE].
R. Bousso and E. Wildenhain, Islands in closed and open universes, Phys. Rev. D 105 (2022) 086012 [arXiv:2202.05278] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2206.06511
Rights and permissions
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.
About this article
Cite this article
Lee, J.H., Neuenfeld, D. & Shukla, A. Bounds on gravitational brane couplings and tomography in AdS3 black hole microstates. J. High Energ. Phys. 2022, 139 (2022). https://doi.org/10.1007/JHEP10(2022)139
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2022)139