Linearity of holographic entanglement entropy

Almheiri, Ahmed; Dong, Xi; Swingle, Brian

doi:10.1007/JHEP02(2017)074

Title: Linearity of holographic entanglement entropy

Journal Article · 13 February 2017 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/JHEP02(2017)074 · OSTI ID:1356081

Almheiri, Ahmed ^[1]; Dong, Xi ^[2]; Swingle, Brian ^[3]

Stanford Univ., Stanford, CA (United States); Stanford University
Institute for Advanced Study, Princeton, NJ (United States)
Stanford Univ., Stanford, CA (United States)

Here, we consider the question of whether the leading contribution to the entanglement entropy in holographic CFTs is truly given by the expectation value of a linear operator as is suggested by the Ryu-Takayanagi formula. We investigate this property by computing the entanglement entropy, via the replica trick, in states dual to superpositions of macroscopically distinct geometries and find it consistent with evaluating the expectation value of the area operator within such states. However, we find that this fails once the number of semi-classical states in the superposition grows exponentially in the central charge of the CFT. Moreover, in certain such scenarios we find that the choice of surface on which to evaluate the area operator depends on the density matrix of the entire CFT. This nonlinearity is enforced in the bulk via the homology prescription of Ryu-Takayanagi. We thus conclude that the homology constraint is not a linear property in the CFT. We also discuss the existence of entropy operators in general systems with a large number of degrees of freedom.

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Research Organization:: Stanford Univ., Stanford, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

Grant/Contract Number:: SC0009988

OSTI ID:: 1356081

Alternate ID(s):: OSTI ID: 1358372; OSTI ID: 22659001

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 2 Vol. 2017; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Local Operators in the Eternal Black Hole Papadodimas, Kyriakos; Raju, Suvrat Physical Review Letters, Vol. 115, Issue 21 https://doi.org/10.1103/physrevlett.115.211601	journal	November 2015
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
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Local Operators in the Eternal Black Hole Papadodimas, Kyriakos; Raju, Suvrat Physical Review Letters, Vol. 115, Issue 21 https://doi.org/10.1103/PhysRevLett.115.211601	journal	November 2015
Black holes and the butterfly effect Shenker, Stephen H.; Stanford, Douglas Journal of High Energy Physics, Vol. 2014, Issue 3 https://doi.org/10.1007/JHEP03(2014)067	journal	March 2014
Black holes: complementarity or firewalls? Almheiri, Ahmed; Marolf, Donald; Polchinski, Joseph Journal of High Energy Physics, Vol. 2013, Issue 2 https://doi.org/10.1007/jhep02(2013)062	journal	February 2013
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Quantum universal variable-length source coding Hayashi, Masahito; Matsumoto, Keiji Physical Review A, Vol. 66, Issue 2 https://doi.org/10.1103/physreva.66.022311	journal	August 2002
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Black holes and the butterfly effect Shenker, Stephen H.; Stanford, Douglas Journal of High Energy Physics, Vol. 2014, Issue 3 https://doi.org/10.1007/jhep03(2014)067	journal	March 2014
The information theoretic interpretation of the length of a curve Czech, Bartlomiej; Hayden, Patrick; Lashkari, Nima Journal of High Energy Physics, Vol. 2015, Issue 6 https://doi.org/10.1007/jhep06(2015)157	journal	June 2015
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The Large-N Limit of Superconformal Field Theories and Supergravity Maldacena, Juan International Journal of Theoretical Physics, Vol. 38, Issue 4, p. 1113-1133 https://doi.org/10.1023/a:1026654312961	journal	January 1999
The holographic entropy cone Bao, Ning; Nezami, Sepehr; Ooguri, Hirosi Journal of High Energy Physics, Vol. 2015, Issue 9 https://doi.org/10.1007/jhep09(2015)130	journal	September 2015
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Causality & holographic entanglement entropy Headrick, Matthew; Hubeny, Veronika E.; Lawrence, Albion arXiv https://doi.org/10.48550/arxiv.1408.6300	text	January 2014
Level-Spacing Distributions and the Airy Kernel Tracy, Craig A.; Widom, Harold arXiv https://doi.org/10.48550/arxiv.hep-th/9210074	text	January 1992
An apologia for firewalls Almheiri, Ahmed; Marolf, Donald; Polchinski, Joseph Journal of High Energy Physics, Vol. 2013, Issue 9 https://doi.org/10.1007/JHEP09(2013)018	journal	September 2013
Cool horizons for entangled black holes Maldacena, Juan; Susskind, Leonard arXiv https://doi.org/10.48550/arxiv.1306.0533	text	January 2013
Generalized gravitational entropy Lewkowycz, Aitor; Maldacena, Juan arXiv https://doi.org/10.48550/arxiv.1304.4926	text	January 2013
The gravity duals of modular Hamiltonians Jafferis, Daniel L.; Suh, S. Josephine Journal of High Energy Physics, Vol. 2016, Issue 9 https://doi.org/10.1007/jhep09(2016)068	journal	September 2016
Bulk and transhorizon measurements in AdS/CFT Heemskerk, Idse; Marolf, Donald; Polchinski, Joseph Journal of High Energy Physics, Vol. 2012, Issue 10 https://doi.org/10.1007/jhep10(2012)165	journal	October 2012

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Title: Linearity of holographic entanglement entropy

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