A bound on holographic entanglement entropy from inverse mean curvature flow

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Title: A bound on holographic entanglement entropy from inverse mean curvature flow
Author(s): Fischetti, S
Wiseman, T
Item Type: Journal Article
Abstract: Entanglement entropies are notoriously difficult to compute. Large-N strongly-coupled holographic CFTs are an important exception, where the AdS/CFT dictionary gives the entanglement entropy of a CFT region in terms of the area of an extremal bulk surface anchored to the AdS boundary. Using this prescription, we show—for quite general states of (2  +  1)-dimensional such CFTs—that the renormalized entanglement entropy of any region of the CFT is bounded from above by a weighted local energy density. The key ingredient in this construction is the inverse mean curvature (IMC) flow, which we suitably generalize to flows of surfaces anchored to the AdS boundary. Our bound can then be thought of as a 'subregion' Penrose inequality in asymptotically locally AdS spacetimes, similar to the Penrose inequalities obtained from IMC flows in asymptotically flat spacetimes. Combining the result with positivity of relative entropy, we argue that our bound is valid perturbatively in 1/N, and conjecture that a restricted version of it holds in any CFT.
Publication Date: 22-May-2017
Date of Acceptance: 3-Apr-2017
URI: http://hdl.handle.net/10044/1/49738
DOI: https://dx.doi.org/10.1088/1361-6382/aa6ad0
ISSN: 0264-9381
Publisher: IOP Publishing
Journal / Book Title: Classical and Quantum Gravity
Volume: 34
Issue: 12
Copyright Statement: © 2017 IOP Publishing Ltd. This is an author-created, un-copyedited version of an article accepted for publication in Classical and Quantum Gravity. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The definitive publisher authenticated version is available online at https://dx.doi.org/10.1088/1361-6382/aa6ad0.
Sponsor/Funder: Science and Technology Facilities Council (STFC)
Funder's Grant Number: ST/L00044X/1
Keywords: Science & Technology
Physical Sciences
Astronomy & Astrophysics
Physics, Multidisciplinary
Physics, Particles & Fields
Physics
AdS/CFT
inverse mean curvature flow
Penrose inequalities
holographic entanglement entropy
entropy bounds
ADS/CFT CORRESPONDENCE
QUANTUM ENTANGLEMENT
PENROSE INEQUALITY
GAUGE-THEORY
C-THEOREM
SPACETIME
hep-th
hep-th
gr-qc
02 Physical Sciences
01 Mathematical Sciences
Nuclear & Particles Physics
Publication Status: Published
Article Number: ARTN 125005
Embargo Date: 2018-05-22
Appears in Collections:Physics
Theoretical Physics
Faculty of Natural Sciences



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