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 · Tue Feb 14 00:00:00 EST 2017 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP02(2017)074· OSTI ID:1358372

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

Stanford Univ., CA (United States). Inst. for Theoretical Physics, Dept. of Physics
Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences

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., CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF); USDOE Office of Science (SC), Basic Energy Sciences (BES)

Contributing Organization:: Princeton Univ., NJ (United States)

Grant/Contract Number:: SC0009988; PHY-1316699

OSTI ID:: 1358372

Alternate ID(s):: OSTI ID: 1356081

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

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 35 works

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Detecting topology change via correlations and entanglement from gauge/gravity correspondence Lin, Hai; Zeng, Keyou Journal of Mathematical Physics, Vol. 59, Issue 3 https://doi.org/10.1063/1.4986985	journal	March 2018
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Holographic Renyi Entropy from Quantum Error Correction Akers, Chris; Rath, Pratik arXiv https://doi.org/10.48550/arxiv.1811.05171	text	January 2018
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Title: Linearity of holographic entanglement entropy

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