Linearity of holographic entanglement entropy
Abstract
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 RyuTakayanagi 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 semiclassical 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 RyuTakayanagi. 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.
 Authors:
 Stanford Univ., Stanford, CA (United States)
 Institute for Advanced Study, Princeton, NJ (United States)
 Publication Date:
 Research Org.:
 Stanford Univ., CA (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC22); USDOE Office of Science (SC), High Energy Physics (HEP) (SC25); National Science Foundation (NSF)
 Contributing Org.:
 Princeton Univ., NJ (United States)
 OSTI Identifier:
 1358372
 Alternate Identifier(s):
 OSTI ID: 1356081
 Grant/Contract Number:
 SC0009988; PHY1316699
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Journal of High Energy Physics (Online)
 Additional Journal Information:
 Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 2; Journal ID: ISSN 10298479
 Publisher:
 Springer Berlin
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; levelspacing distributions; blackholes; airy kernel; quantum; system; states; AdSCFT correspondence; black holes in string theory; gaugegravity correspondence; conformal field theory; AdSCFT Correspondence
Citation Formats
Almheiri, Ahmed, Dong, Xi, and Swingle, Brian. Linearity of holographic entanglement entropy. United States: N. p., 2017.
Web. doi:10.1007/JHEP02(2017)074.
Almheiri, Ahmed, Dong, Xi, & Swingle, Brian. Linearity of holographic entanglement entropy. United States. doi:10.1007/JHEP02(2017)074.
Almheiri, Ahmed, Dong, Xi, and Swingle, Brian. Tue .
"Linearity of holographic entanglement entropy". United States.
doi:10.1007/JHEP02(2017)074. https://www.osti.gov/servlets/purl/1358372.
@article{osti_1358372,
title = {Linearity of holographic entanglement entropy},
author = {Almheiri, Ahmed and Dong, Xi and Swingle, Brian},
abstractNote = {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 RyuTakayanagi 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 semiclassical 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 RyuTakayanagi. 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.},
doi = {10.1007/JHEP02(2017)074},
journal = {Journal of High Energy Physics (Online)},
number = 2,
volume = 2017,
place = {United States},
year = {Tue Feb 14 00:00:00 EST 2017},
month = {Tue Feb 14 00:00:00 EST 2017}
}
Web of Science

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 RyuTakayanagi 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 semiclassical states in the superposition grows exponentially in the central charge of the CFT. Moreover, in certainmore »Cited by 4

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