Deriving covariant holographic entanglement

Dong, Xi; Lewkowycz, Aitor; Rangamani, Mukund

doi:10.1007/JHEP11(2016)028

Deriving covariant holographic entanglement

Journal Article · Mon Nov 07 00:00:00 EST 2016 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP11(2016)028· OSTI ID:1597743

Dong, Xi ^[1]; Lewkowycz, Aitor ^[2]; Rangamani, Mukund ^[3]

Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences; Institute for Advanced Study
Princeton Univ., NJ (United States)
Univ. of California, Davis, CA (United States)

We provide a gravitational argument in favour of the covariant holographic entanglement entropy proposal. In general time-dependent states, the proposal asserts that the entanglement entropy of a region in the boundary field theory is given by a quarter of the area of a bulk extremal surface in Planck units. The main element of our discussion is an implementation of an appropriate Schwinger-Keldysh contour to obtain the reduced density matrix (and its powers) of a given region, as is relevant for the replica construction. We map this contour into the bulk gravitational theory, and argue that the saddle point solutions of these replica geometries lead to a consistent prescription for computing the field theory Rényi entropies. In the limiting case where the replica index is taken to unity, a local analysis suffices to show that these saddles lead to the extremal surfaces of interest. We also comment on various properties of holographic entanglement that follow from this construction.

View Accepted Manuscript (DOE)

Research Organization:: Inst. for Advanced Study, Princeton, NJ (United States)

Sponsoring Organization:: National Science Foundation (NSF); USDOE Office of Science (SC)

Grant/Contract Number:: SC0009988

OSTI ID:: 1597743

Alternate ID(s):: OSTI ID: 22612853

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 11 Vol. 2016; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

References (56)

The Theory of a General Quantum System Interacting with a Linear Dissipative System Feynman, R. P.; Vernon, F. L. Annals of Physics, Vol. 281, Issue 1-2 https://doi.org/10.1006/aphy.2000.6017	journal	April 2000
Holographic entanglement entropy for general higher derivative gravity Dong, Xi Journal of High Energy Physics, Vol. 2014, Issue 1 https://doi.org/10.1007/JHEP01(2014)044	journal	January 2014
The fluid manifesto: emergent symmetries, hydrodynamics, and black holes Haehl, Felix M.; Loganayagam, R.; Rangamani, Mukund Journal of High Energy Physics, Vol. 2016, Issue 1 https://doi.org/10.1007/JHEP01(2016)184	journal	January 2016
Generalized entropy and higher derivative gravity Camps, Joan Journal of High Energy Physics, Vol. 2014, Issue 3 https://doi.org/10.1007/JHEP03(2014)070	journal	March 2014
General properties of holographic entanglement entropy Headrick, Matthew Journal of High Energy Physics, Vol. 2014, Issue 3 https://doi.org/10.1007/JHEP03(2014)085	journal	March 2014
Generalized gravitational entropy without replica symmetry Camps, Joan; Kelly, William R. Journal of High Energy Physics, Vol. 2015, Issue 3 https://doi.org/10.1007/JHEP03(2015)061	journal	March 2015
The imaginary part of the gravity action and black hole entropy Neiman, Yasha Journal of High Energy Physics, Vol. 2013, Issue 4 https://doi.org/10.1007/JHEP04(2013)071	journal	April 2013
Entanglement entropy in three dimensional gravity Maxfield, Henry Journal of High Energy Physics, Vol. 2015, Issue 4 https://doi.org/10.1007/JHEP04(2015)031	journal	April 2015
Bulk locality and quantum error correction in AdS/CFT Almheiri, Ahmed; Dong, Xi; Harlow, Daniel Journal of High Energy Physics, Vol. 2015, Issue 4 https://doi.org/10.1007/JHEP04(2015)163	journal	April 2015
Towards a derivation of holographic entanglement entropy Casini, Horacio; Huerta, Marina; Myers, Robert C. Journal of High Energy Physics, Vol. 2011, Issue 5 https://doi.org/10.1007/JHEP05(2011)036	journal	May 2011
Topological aspects of generalized gravitational entropy Haehl, Felix M.; Hartman, Thomas; Marolf, Donald Journal of High Energy Physics, Vol. 2015, Issue 5 https://doi.org/10.1007/JHEP05(2015)023	journal	May 2015
Causal holographic information Hubeny, Veronika E.; Rangamani, Mukund Journal of High Energy Physics, Vol. 2012, Issue 6 https://doi.org/10.1007/JHEP06(2012)114	journal	June 2012
Relative entropy equals bulk relative entropy Jafferis, Daniel L.; Lewkowycz, Aitor; Maldacena, Juan Journal of High Energy Physics, Vol. 2016, Issue 6 https://doi.org/10.1007/JHEP06(2016)004	journal	June 2016
Generalized gravitational entropy Lewkowycz, Aitor; Maldacena, Juan Journal of High Energy Physics, Vol. 2013, Issue 8 https://doi.org/10.1007/JHEP08(2013)090	journal	August 2013
Covariant residual entropy Hubeny, Veronika E. Journal of High Energy Physics, Vol. 2014, Issue 9 https://doi.org/10.1007/JHEP09(2014)156	journal	September 2014
Quantum corrections to holographic entanglement entropy Faulkner, Thomas; Lewkowycz, Aitor; Maldacena, Juan Journal of High Energy Physics, Vol. 2013, Issue 11 https://doi.org/10.1007/JHEP11(2013)074	journal	November 2013
Holographic calculations of Rényi entropy Hung, Ling-Yan; Myers, Robert C.; Smolkin, Michael Journal of High Energy Physics, Vol. 2011, Issue 12 https://doi.org/10.1007/JHEP12(2011)047	journal	December 2011
Causality & holographic entanglement entropy Headrick, Matthew; Hubeny, Veronika E.; Lawrence, Albion Journal of High Energy Physics, Vol. 2014, Issue 12 https://doi.org/10.1007/JHEP12(2014)162	journal	December 2014
The theory of a general quantum system interacting with a linear dissipative system Feynman, R. P.; Vernon, F. L. Annals of Physics, Vol. 24 https://doi.org/10.1016/0003-4916(63)90068-X	journal	October 1963
Is it possible to create a universe in the laboratory by quantum tunneling? Farhi, Edward; Guth, Alan H.; Guven, Jemal Nuclear Physics B, Vol. 339, Issue 2 https://doi.org/10.1016/0550-3213(90)90357-J	journal	July 1990
The gravity dual of Rényi entropy Dong, Xi Nature Communications, Vol. 7, Issue 1 https://doi.org/10.1038/ncomms12472	journal	August 2016
Brownian Motion of a Quantum Oscillator Schwinger, Julian Journal of Mathematical Physics, Vol. 2, Issue 3 https://doi.org/10.1063/1.1703727	journal	May 1961
The gravity dual of a density matrix Czech, Bartłomiej; Karczmarek, Joanna L.; Nogueira, Fernando Classical and Quantum Gravity, Vol. 29, Issue 15 https://doi.org/10.1088/0264-9381/29/15/155009	journal	July 2012
Complex entangling surfaces for AdS and Lifshitz black holes? Fischetti, Sebastian; Marolf, Donald Classical and Quantum Gravity, Vol. 31, Issue 21 https://doi.org/10.1088/0264-9381/31/21/214005	journal	October 2014
Maximin surfaces, and the strong subadditivity of the covariant holographic entanglement entropy Wall, Aron C. Classical and Quantum Gravity, Vol. 31, Issue 22 https://doi.org/10.1088/0264-9381/31/22/225007	journal	November 2014
A paucity of bulk entangling surfaces: AdS wormholes with de Sitter interiors Fischetti, Sebastian; Marolf, Donald; Wall, Aron C. Classical and Quantum Gravity, Vol. 32, Issue 6 https://doi.org/10.1088/0264-9381/32/6/065011	journal	February 2015
Spacelike branes Gutperle, Michael; Strominger, Andrew Journal of High Energy Physics, Vol. 2002, Issue 04 https://doi.org/10.1088/1126-6708/2002/04/018	journal	April 2002
Minkowski-space correlators in AdS/CFT correspondence: recipe and applications Son, Dam T.; Starinets, Andrei O. Journal of High Energy Physics, Vol. 2002, Issue 09 https://doi.org/10.1088/1126-6708/2002/09/042	journal	September 2002
Schwinger-Keldysh propagators from AdS/CFT correspondence Herzog, Christopher P.; Son, Dam Thanh Journal of High Energy Physics, Vol. 2003, Issue 03 https://doi.org/10.1088/1126-6708/2003/03/046	journal	March 2003
Eternal black holes in anti-de Sitter Maldacena, Juan Journal of High Energy Physics, Vol. 2003, Issue 04 https://doi.org/10.1088/1126-6708/2003/04/021	journal	April 2003
Aspects of holographic entanglement entropy Ryu, Shinsei; Takayanagi, Tadashi Journal of High Energy Physics, Vol. 2006, Issue 08 https://doi.org/10.1088/1126-6708/2006/08/045	journal	August 2006
Proof of the holographic formula for entanglement entropy Fursaev, Dmitri V. Journal of High Energy Physics, Vol. 2006, Issue 09 https://doi.org/10.1088/1126-6708/2006/09/018	journal	September 2006
A covariant holographic entanglement entropy proposal Hubeny, Veronika E.; Rangamani, Mukund; Takayanagi, Tadashi Journal of High Energy Physics, Vol. 2007, Issue 07 https://doi.org/10.1088/1126-6708/2007/07/062	journal	July 2007
Remarks on the entanglement entropy for disconnected regions Casini, H.; Huerta, M. Journal of High Energy Physics, Vol. 2009, Issue 03 https://doi.org/10.1088/1126-6708/2009/03/048	journal	March 2009
Real-time gauge/gravity duality: prescription, renormalization and examples Skenderis, Kostas; Rees, Balt C. van Journal of High Energy Physics, Vol. 2009, Issue 05 https://doi.org/10.1088/1126-6708/2009/05/085	journal	May 2009
Some properties of the Noether charge and a proposal for dynamical black hole entropy Iyer, Vivek; Wald, Robert M. Physical Review D, Vol. 50, Issue 2 https://doi.org/10.1103/PhysRevD.50.846	journal	July 1994
Real-Time Gauge/Gravity Duality Skenderis, Kostas; van Rees, Balt C. Physical Review Letters, Vol. 101, Issue 8 https://doi.org/10.1103/PhysRevLett.101.081601	journal	August 2008
Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality Dong, Xi; Harlow, Daniel; Wall, Aron C. Physical Review Letters, Vol. 117, Issue 2 https://doi.org/10.1103/PhysRevLett.117.021601	journal	July 2016
Holographic Derivation of Entanglement Entropy from the anti–de Sitter Space/Conformal Field Theory Correspondence Ryu, Shinsei; Takayanagi, Tadashi Physical Review Letters, Vol. 96, Issue 18 https://doi.org/10.1103/PhysRevLett.96.181602	journal	May 2006
Brownian motion of a quantum oscillator Carusotto, Salvatore Physical Review A, Vol. 11, Issue 4 https://doi.org/10.1103/physreva.11.1397	journal	April 1975
A Second Law for higher curvature gravity Wall, Aron C. International Journal of Modern Physics D, Vol. 24, Issue 12 https://doi.org/10.1142/S0218271815440149	journal	October 2015
Anti de Sitter space and holography Witten, Edward Advances in Theoretical and Mathematical Physics, Vol. 2, Issue 2 https://doi.org/10.4310/ATMP.1998.v2.n2.a2	journal	January 1998
A Covariant Holographic Entanglement Entropy Proposal Hubeny, Veronika E.; Rangamani, Mukund; Takayanagi, Tadashi arXiv https://doi.org/10.48550/arxiv.0705.0016	text	January 2007
Real-time gauge/gravity duality Skenderis, Kostas; van Rees, Balt C. arXiv https://doi.org/10.48550/arxiv.0805.0150	text	January 2008
Real-time gauge/gravity duality: Prescription, Renormalization and Examples Skenderis, Kostas; van Rees, Balt C. arXiv https://doi.org/10.48550/arxiv.0812.2909	text	January 2008
Towards a derivation of holographic entanglement entropy Casini, Horacio; Huerta, Marina; Myers, Robert C. arXiv https://doi.org/10.48550/arxiv.1102.0440	text	January 2011
The imaginary part of the gravity action and black hole entropy Neiman, Yasha arXiv https://doi.org/10.48550/arxiv.1301.7041	text	January 2013
Generalized gravitational entropy Lewkowycz, Aitor; Maldacena, Juan arXiv https://doi.org/10.48550/arxiv.1304.4926	text	January 2013
Quantum corrections to holographic entanglement entropy Faulkner, Thomas; Lewkowycz, Aitor; Maldacena, Juan arXiv https://doi.org/10.48550/arxiv.1307.2892	text	January 2013
Holographic Entanglement Entropy for General Higher Derivative Gravity Dong, Xi arXiv https://doi.org/10.48550/arxiv.1310.5713	text	January 2013
General properties of holographic entanglement entropy Headrick, Matthew arXiv https://doi.org/10.48550/arxiv.1312.6717	text	January 2013
Causality & holographic entanglement entropy Headrick, Matthew; Hubeny, Veronika E.; Lawrence, Albion arXiv https://doi.org/10.48550/arxiv.1408.6300	text	January 2014
Topological aspects of generalized gravitational entropy Haehl, Felix M.; Hartman, Thomas; Marolf, Donald arXiv https://doi.org/10.48550/arxiv.1412.7561	text	January 2014
Spacelike Branes Gutperle, Michael; Strominger, Andrew arXiv https://doi.org/10.48550/arxiv.hep-th/0202210	text	January 2002
Aspects of Holographic Entanglement Entropy Ryu, Shinsei; Takayanagi, Tadashi arXiv https://doi.org/10.48550/arxiv.hep-th/0605073	text	January 2006
Anti De Sitter Space And Holography Witten, Edward arXiv https://doi.org/10.48550/arxiv.hep-th/9802150	text	January 1998

Cited By (57)

Entropy, extremality, euclidean variations, and the equations of motion Dong, Xi; Lewkowycz, Aitor Journal of High Energy Physics, Vol. 2018, Issue 1 https://doi.org/10.1007/jhep01(2018)081	journal	January 2018
Modifications to holographic entanglement entropy in warped CFT Song, Wei; Wen, Qiang; Xu, Jianfei Journal of High Energy Physics, Vol. 2017, Issue 2 https://doi.org/10.1007/jhep02(2017)067	journal	February 2017
Comments on holographic complexity Carmi, Dean; Myers, Robert C.; Rath, Pratik Journal of High Energy Physics, Vol. 2017, Issue 3 https://doi.org/10.1007/jhep03(2017)118	journal	March 2017
All the entropies on the light-cone Casini, Horacio; Testé, Eduardo; Torroba, Gonzalo Journal of High Energy Physics, Vol. 2018, Issue 5 https://doi.org/10.1007/jhep05(2018)005	journal	May 2018
Geometric aspects of holographic bit threads Agón, Cesar A.; de Boer, Jan; Pedraza, Juan F. Journal of High Energy Physics, Vol. 2019, Issue 5 https://doi.org/10.1007/jhep05(2019)075	journal	May 2019
Restricted Maximin surfaces and HRT in generic black hole spacetimes Marolf, Donald; Wall, Aron C.; Wang, Zhencheng Journal of High Energy Physics, Vol. 2019, Issue 5 https://doi.org/10.1007/jhep05(2019)127	journal	May 2019
Coarse graining holographic black holes Engelhardt, Netta; Wall, Aron C. Journal of High Energy Physics, Vol. 2019, Issue 5 https://doi.org/10.1007/jhep05(2019)160	journal	May 2019
Holographic subregion complexity under a thermal quench Chen, Bin; Li, Wen-Ming; Yang, Run-Qiu Journal of High Energy Physics, Vol. 2018, Issue 7 https://doi.org/10.1007/jhep07(2018)034	journal	July 2018
Holographic second laws of black hole thermodynamics Bernamonti, Alice; Galli, Federico; Myers, Robert C. Journal of High Energy Physics, Vol. 2018, Issue 7 https://doi.org/10.1007/jhep07(2018)111	journal	July 2018
Circuit complexity for free fermions Hackl, Lucas; Myers, Robert C. Journal of High Energy Physics, Vol. 2018, Issue 7 https://doi.org/10.1007/jhep07(2018)139	journal	July 2018
Holographic coherent states from random tensor networks Qi, Xiao-Liang; Yang, Zhao; You, Yi-Zhuang Journal of High Energy Physics, Vol. 2017, Issue 8 https://doi.org/10.1007/jhep08(2017)060	journal	August 2017
Rényi entropy at large energy density in 2D CFT Guo, Wu-zhong; Lin, Feng-Li; Zhang, Jiaju Journal of High Energy Physics, Vol. 2019, Issue 8 https://doi.org/10.1007/jhep08(2019)010	journal	August 2019
Microcanonical path integrals and the holography of small black hole interiors Marolf, Donald Journal of High Energy Physics, Vol. 2018, Issue 9 https://doi.org/10.1007/jhep09(2018)114	journal	September 2018
Circuit complexity in quantum field theory Jefferson, Robert A.; Myers, Robert C. Journal of High Energy Physics, Vol. 2017, Issue 10 https://doi.org/10.1007/jhep10(2017)107	journal	October 2017
Rényi mutual information in holographic warped CFTs Chen, Bin; Hao, Peng-Xiang; Song, Wei Journal of High Energy Physics, Vol. 2019, Issue 10 https://doi.org/10.1007/jhep10(2019)037	journal	October 2019
Subsystem trace distance in low-lying states of (1 + 1)-dimensional conformal field theories Zhang, Jiaju; Ruggiero, Paola; Calabrese, Pasquale Journal of High Energy Physics, Vol. 2019, Issue 10 https://doi.org/10.1007/jhep10(2019)181	journal	October 2019
Renormalized AdS gravity and holographic entanglement entropy of even-dimensional CFTs Anastasiou, Giorgos; Araya, Ignacio J.; Güijosa, Alberto Journal of High Energy Physics, Vol. 2019, Issue 10 https://doi.org/10.1007/jhep10(2019)221	journal	October 2019
Flat entanglement spectra in fixed-area states of quantum gravity Dong, Xi; Harlow, Daniel; Marolf, Donald Journal of High Energy Physics, Vol. 2019, Issue 10 https://doi.org/10.1007/jhep10(2019)240	journal	October 2019
On the time dependence of holographic complexity Carmi, Dean; Chapman, Shira; Marrochio, Hugo Journal of High Energy Physics, Vol. 2017, Issue 11 https://doi.org/10.1007/jhep11(2017)188	journal	November 2017
On the role of counterterms in holographic complexity Akhavan, Amin; Omidi, Farzad Journal of High Energy Physics, Vol. 2019, Issue 11 https://doi.org/10.1007/jhep11(2019)054	journal	November 2019
Constraining higher order gravities with subregion duality Cáceres, Elena; Misobuchi, Anderson Seigo; Pedraza, Juan F. Journal of High Energy Physics, Vol. 2019, Issue 11 https://doi.org/10.1007/jhep11(2019)175	journal	November 2019
Barrier from chaos: operator entanglement dynamics of the reduced density matrix Wang, Huajia; Zhou, Tianci Journal of High Energy Physics, Vol. 2019, Issue 12 https://doi.org/10.1007/jhep12(2019)020	journal	December 2019
Gravitation in flat spacetime from entanglement Godet, Victor; Marteau, Charles Journal of High Energy Physics, Vol. 2019, Issue 12 https://doi.org/10.1007/jhep12(2019)057	journal	December 2019
The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole Almheiri, Ahmed; Engelhardt, Netta; Marolf, Donald Journal of High Energy Physics, Vol. 2019, Issue 12 https://doi.org/10.1007/jhep12(2019)063	journal	December 2019
The Ryu–Takayanagi Formula from Quantum Error Correction Harlow, Daniel Communications in Mathematical Physics, Vol. 354, Issue 3 https://doi.org/10.1007/s00220-017-2904-z	journal	May 2017
The quantum null energy condition in curved space Fu, Zicao; Koeller, Jason; Marolf, Donald Classical and Quantum Gravity, Vol. 34, Issue 22 https://doi.org/10.1088/1361-6382/aa8f2c	journal	October 2017
Metric perturbations of extremal surfaces Mosk, Benjamin Classical and Quantum Gravity, Vol. 35, Issue 4 https://doi.org/10.1088/1361-6382/aaa4e9	journal	January 2018
Towards bulk metric reconstruction from extremal area variations Bao, Ning; Cao, ChunJun; Fischetti, Sebastian Classical and Quantum Gravity, Vol. 36, Issue 18 https://doi.org/10.1088/1361-6382/ab377f	journal	August 2019
Quantum and classical correlations inside the entanglement wedge Umemoto, Koji Physical Review D, Vol. 100, Issue 12 https://doi.org/10.1103/physrevd.100.126021	journal	December 2019
Holographic entropy cone in AdS-Vaidya spacetimes Caginalp, Reginald J. Physical Review D, Vol. 101, Issue 2 https://doi.org/10.1103/physrevd.101.026010	journal	January 2020
Boundary dual of bulk local operators Sanches, Fabio; Weinberg, Sean J. Physical Review D, Vol. 96, Issue 2 https://doi.org/10.1103/physrevd.96.026004	journal	July 2017
First law of entanglement rates from holography O’Bannon, Andy; Probst, Jonas; Rodgers, Ronnie Physical Review D, Vol. 96, Issue 6 https://doi.org/10.1103/physrevd.96.066028	journal	September 2017
Decoding the Apparent Horizon: Coarse-Grained Holographic Entropy Engelhardt, Netta; Wall, Aron C. Physical Review Letters, Vol. 121, Issue 21 https://doi.org/10.1103/physrevlett.121.211301	journal	November 2018
Constraints on Symmetries from Holography Harlow, Daniel; Ooguri, Hirosi Physical Review Letters, Vol. 122, Issue 19 https://doi.org/10.1103/physrevlett.122.191601	journal	May 2019
Path Integral Optimization as Circuit Complexity Camargo, Hugo A.; Heller, Michal P.; Jefferson, Ro Physical Review Letters, Vol. 123, Issue 1 https://doi.org/10.1103/physrevlett.123.011601	journal	July 2019
Entanglement entropy: Holography and renormalization group Nishioka, Tatsuma Reviews of Modern Physics, Vol. 90, Issue 3 https://doi.org/10.1103/revmodphys.90.035007	journal	September 2018
What’s the point? Hole-ography in Poincaré AdS Espíndola, Ricardo; Güijosa, Alberto; Landetta, Alberto The European Physical Journal C, Vol. 78, Issue 1 https://doi.org/10.1140/epjc/s10052-018-5563-0	journal	January 2018
Entanglement wedge reconstruction and entanglement of purification Espíndola, Ricardo; Güijosa, Alberto; Pedraza, Juan F. The European Physical Journal C, Vol. 78, Issue 8 https://doi.org/10.1140/epjc/s10052-018-6140-2	journal	August 2018
Covariant holographic entanglement negativity for disjoint intervals in $$AdS_3/CFT_2$$ A d S 3 / C F T 2 Malvimat, Vinay; Mondal, Sayid; Paul, Boudhayan The European Physical Journal C, Vol. 79, Issue 6 https://doi.org/10.1140/epjc/s10052-019-7032-9	journal	June 2019
Classification of out-of-time-order correlators Haehl, Felix; Loganayagam, R.; Narayan, Prithvi SciPost Physics, Vol. 6, Issue 1 https://doi.org/10.21468/scipostphys.6.1.001	journal	January 2019
The Ryu-Takayanagi Formula from Quantum Error Correction Harlow, Daniel arXiv https://doi.org/10.48550/arxiv.1607.03901	text	January 2016
Modifications to Holographic Entanglement Entropy in Warped CFT Song, Wei; Wen, Qiang; Xu, Jianfei arXiv https://doi.org/10.48550/arxiv.1610.00727	text	January 2016
Classification of out-of-time-order correlators Haehl, Felix M.; Loganayagam, R.; Narayan, Prithvi arXiv https://doi.org/10.48550/arxiv.1701.02820	text	January 2017
Holographic coherent states from random tensor networks Qi, Xiao-Liang; Yang, Zhao; You, Yi-Zhuang arXiv https://doi.org/10.48550/arxiv.1703.06533	text	January 2017
The Quantum Null Energy Condition in Curved Space Fu, Zicao; Koeller, Jason; Marolf, Donald arXiv https://doi.org/10.48550/arxiv.1706.01572	text	January 2017
What's the Point? Hole-ography in Poincare AdS Espíndola, Ricardo; Guijosa, Alberto; Landetta, Alberto arXiv https://doi.org/10.48550/arxiv.1708.02958	text	January 2017
On the Time Dependence of Holographic Complexity Carmi, Dean; Chapman, Shira; Marrochio, Hugo arXiv https://doi.org/10.48550/arxiv.1709.10184	text	January 2017
Metric Perturbations of Extremal Surfaces Mosk, Benjamin arXiv https://doi.org/10.48550/arxiv.1710.01316	text	January 2017
Entanglement Wedge Reconstruction and Entanglement of Purification Espíndola, Ricardo; Guijosa, Alberto; Pedraza, Juan F. arXiv https://doi.org/10.48550/arxiv.1804.05855	text	January 2018
Constraints on symmetry from holography Harlow, Daniel; Ooguri, Hirosi arXiv https://doi.org/10.48550/arxiv.1810.05337	text	January 2018
Flat entanglement spectra in fixed-area states of quantum gravity Dong, Xi; Harlow, Daniel; Marolf, Donald arXiv https://doi.org/10.48550/arxiv.1811.05382	text	January 2018
Geometric Aspects of Holographic Bit Threads Agón, Cesar A.; de Boer, Jan; Pedraza, Juan F. arXiv https://doi.org/10.48550/arxiv.1811.08879	text	January 2018
Path integral optimization as circuit complexity Camargo, Hugo A.; Heller, Michal P.; Jefferson, Ro arXiv https://doi.org/10.48550/arxiv.1904.02713	text	January 2019
Towards Bulk Metric Reconstruction from Extremal Area Variations Bao, Ning; Cao, ChunJun; Fischetti, Sebastian arXiv https://doi.org/10.48550/arxiv.1904.04834	text	January 2019
The Holographic Entropy Cone in AdS-Vaidya Spacetimes Caginalp, Reginald J. arXiv https://doi.org/10.48550/arxiv.1905.00544	text	January 2019
The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole Almheiri, Ahmed; Engelhardt, Netta; Marolf, Donald arXiv https://doi.org/10.48550/arxiv.1905.08762	text	January 2019
Renormalized AdS gravity and holographic entanglement entropy of even-dimensional CFTs Anastasiou, Giorgos; Araya, Ignacio J.; Guijosa, Alberto arXiv https://doi.org/10.48550/arxiv.1908.11447	text	January 2019

Similar Records

Entanglement negativity and replica symmetry breaking in general holographic states

Journal Article · Wed Jan 01 19:00:00 EST 2025 · Journal of High Energy Physics · OSTI ID:2999778

Diagonal Approximation for Holographic Rényi Entropies

Journal Article · Tue Apr 22 20:00:00 EDT 2025 · Physical Review Letters · OSTI ID:2562176

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
AdS-CFT Correspondence
Classical Theories of Gravity
Gauge-gravity correspondence

Deriving covariant holographic entanglement

Citation Formats

References (56)

Cited By (57)

Similar Records

Related Subjects