Abstract
Recent works have suggested that the entanglement wedge of Hawking radiation coming from an AdS black hole will include an island inside the black hole interior after the Page time. In this paper, we propose a concrete way to extract the information from the island by acting only on the radiation degrees of freedom, building on the equivalence between the boundary and bulk modular flow. We consider examples with black holes in JT gravity coupled to baths. In the case that the bulk conformal fields contain free massless fermion field, we provide explicit bulk picture of the information extraction process, where we find that one can almost pull out an operator from the island to the bath with modular flow.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
G. Penington, Entanglement wedge reconstruction and the information paradox, arXiv:1905.08255 [INSPIRE].
A. Almheiri, N. Engelhardt, D. Marolf and H. Maxfield, The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole, JHEP 12 (2019) 063 [arXiv:1905.08762] [INSPIRE].
A. Almheiri, R. Mahajan, J. Maldacena and Y. Zhao, The Page curve of Hawking radiation from semiclassical geometry, arXiv:1908.10996 [INSPIRE].
D.N. Page, Information in black hole radiation, Phys. Rev. Lett. 71 (1993) 3743 [hep-th/9306083] [INSPIRE].
D.N. Page, Time dependence of Hawking radiation entropy, JCAP 09 (2013) 028 [arXiv:1301.4995] [INSPIRE].
C. Akers, S. Leichenauer and A. Levine, Large breakdowns of entanglement wedge reconstruction, Phys. Rev. D 100 (2019) 126006 [arXiv:1908.03975] [INSPIRE].
Z. Fu and D. Marolf, Bag-of-gold spacetimes, Euclidean wormholes and inflation from domain walls in AdS/CFT, JHEP 11 (2019) 040 [arXiv:1909.02505] [INSPIRE].
C. Akers, N. Engelhardt and D. Harlow, Simple holographic models of black hole evaporation, arXiv:1910.00972 [INSPIRE].
A. Almheiri, R. Mahajan and J. Maldacena, Islands outside the horizon, arXiv:1910.11077 [INSPIRE].
M. Rozali et al., Information radiation in BCFT models of black holes, arXiv:1910.12836 [INSPIRE].
R. Bousso and M. Tomašević, Unitarity from a smooth horizon?, arXiv:1911.06305 [INSPIRE].
A. Almheiri, R. Mahajan and J.E. Santos, Entanglement islands in higher dimensions, arXiv:1911.09666 [INSPIRE].
Y. Zhao, A quantum circuit interpretation of evaporating black hole geometry, arXiv:1912.00909 [INSPIRE].
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
V.E. Hubeny, M. Rangamani and T. Takayanagi, A covariant holographic entanglement entropy proposal, JHEP 07 (2007) 062 [arXiv:0705.0016] [INSPIRE].
T. Faulkner, A. Lewkowycz and J. Maldacena, Quantum corrections to holographic entanglement entropy, JHEP 11 (2013) 074 [arXiv:1307.2892] [INSPIRE].
N. Engelhardt and A.C. Wall, Quantum extremal surfaces: holographic entanglement entropy beyond the classical regime, JHEP 01 (2015) 073 [arXiv:1408.3203] [INSPIRE].
S.W. Hawking, Particle creation by black holes, Commun. Math. Phys. 43 (1975) 199 [Erratum ibid. 46 (1976) 206] [INSPIRE].
A. Almheiri et al., Replica wormholes and the entropy of Hawking radiation, arXiv:1911.12333 [INSPIRE].
G. Penington, S.H. Shenker, D. Stanford and Z. Yang, Replica wormholes and the black hole interior, arXiv:1911.11977 [INSPIRE].
B. Czech, J.L. Karczmarek, F. Nogueira and M. Van Raamsdonk, The gravity dual of a density matrix, Class. Quant. Grav. 29 (2012) 155009 [arXiv:1204.1330] [INSPIRE].
M. Headrick, V.E. Hubeny, A. Lawrence and M. Rangamani, Causality & holographic entanglement entropy, JHEP 12 (2014) 162 [arXiv:1408.6300] [INSPIRE].
X. Dong, D. Harlow and A.C. Wall, Reconstruction of bulk operators within the entanglement wedge in gauge-gravity duality, Phys. Rev. Lett. 117 (2016) 021601 [arXiv:1601.05416] [INSPIRE].
D.L. Jafferis and S.J. Suh, The gravity duals of modular hamiltonians, JHEP 09 (2016) 068 [arXiv:1412.8465] [INSPIRE].
D.L. Jafferis, A. Lewkowycz, J. Maldacena and S.J. Suh, Relative entropy equals bulk relative entropy, JHEP 06 (2016) 004 [arXiv:1512.06431] [INSPIRE].
D. Harlow, The Ryu–Takayanagi formula from quantum error correction, Commun. Math. Phys. 354 (2017) 865 [arXiv:1607.03901] [INSPIRE].
X. Dong and A. Lewkowycz, Entropy, extremality, Euclidean variations and the equations of motion, JHEP 01 (2018) 081 [arXiv:1705.08453] [INSPIRE].
X. Dong and D. Marolf, One-loop universality of holographic codes, arXiv:1910.06329 [INSPIRE].
T. Faulkner and A. Lewkowycz, Bulk locality from modular flow, JHEP 07 (2017) 151 [arXiv:1704.05464] [INSPIRE].
A. Almheiri, T. Anous and A. Lewkowycz, Inside out: meet the operators inside the horizon. On bulk reconstruction behind causal horizons, JHEP 01 (2018) 028 [arXiv:1707.06622] [INSPIRE].
Y. Chen, X. Dong, A. Lewkowycz and X.-L. Qi, Modular flow as a disentangler, JHEP 12 (2018) 083 [arXiv:1806.09622] [INSPIRE].
T. Faulkner, M. Li and H. Wang, A modular toolkit for bulk reconstruction, JHEP 04 (2019) 119 [arXiv:1806.10560] [INSPIRE].
H. Casini and M. Huerta, Reduced density matrix and internal dynamics for multicomponent regions, Class. Quant. Grav. 26 (2009) 185005 [arXiv:0903.5284] [INSPIRE].
J. Cotler et al., Entanglement Wedge reconstruction via universal recovery channels, Phys. Rev. X 9 (2019) 031011 [arXiv:1704.05839] [INSPIRE].
C.-F. Chen, G. Penington and G. Salton, Entanglement wedge reconstruction using the Petz map, JHEP 01 (2020) 168 [arXiv:1902.02844] [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.
A. Almheiri and J. Polchinski, Models of AdS2 backreaction and holography, JHEP 11 (2015) 014 [arXiv:1402.6334] [INSPIRE].
A. Almheiri, Holographic quantum error correction and the projected black hole interior, arXiv:1810.02055 [INSPIRE].
R. Longo, P. Martinetti and K.-H. Rehren, Geometric modular action for disjoint intervals and boundary conformal field theory, Rev. Math. Phys. 22 (2010) 331 [arXiv:0912.1106] [INSPIRE].
T. Banks, M.R. Douglas, G.T. Horowitz and E.J. Martinec, AdS dynamics from conformal field theory, hep-th/9808016 [INSPIRE].
A. Hamilton, D.N. Kabat, G. Lifschytz and D.A. Lowe, Holographic representation of local bulk operators, Phys. Rev. D 74 (2006) 066009 [hep-th/0606141] [INSPIRE].
P. Hayden and J. Preskill, Black holes as mirrors: quantum information in random subsystems, JHEP 09 (2007) 120 [arXiv:0708.4025] [INSPIRE].
R.E. Arias, H. Casini, M. Huerta and D. Pontello, Entropy and modular Hamiltonian for a free chiral scalar in two intervals, Phys. Rev. D 98 (2018) 125008 [arXiv:1809.00026] [INSPIRE].
P. Gao, D.L. Jafferis and A.C. Wall, Traversable wormholes via a double trace deformation, JHEP 12 (2017) 151 [arXiv:1608.05687] [INSPIRE].
J. Maldacena, D. Stanford and Z. Yang, Diving into traversable wormholes, Fortsch. Phys. 65 (2017) 1700034 [arXiv:1704.05333] [INSPIRE].
J. Maldacena and L. Susskind, Cool horizons for entangled black holes, Fortsch. Phys. 61 (2013) 781 [arXiv:1306.0533] [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: 1912.02210
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
Chen, Y. Pulling out the island with modular flow. J. High Energ. Phys. 2020, 33 (2020). https://doi.org/10.1007/JHEP03(2020)033
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2020)033