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Bounds on the local energy density of holographic CFTs from bulk geometry

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Title: Bounds on the local energy density of holographic CFTs from bulk geometry
Authors: Fischetti, S
Hickling, A
Wiseman, TAJ
Item Type: Journal Article
Abstract: The stress tensor is a basic local operator in any field theory; in the context of AdS/CFT, it is the operator which is dual to the bulk geometry itself. Here we exploit this feature by using the bulk geometry to place constraints on the local energy density in static states of holographic (2+ 1)- dimensional CFTs living on a closed (but otherwise generally curved) spatial geometry. We allow for the presence of a marginal scalar deformation, dual to a massless scalar field in the bulk. For certain vacuum states in which the bulk geometry is well-behaved at zero temperature, we find that the bulk equations of motion imply that the local energy density integrated over specific boundary domains is negative. In the absence of scalar deformations, we use the inverse mean curvature flow to show that if the CFT spatial geometry has spherical topology but non-constant curvature, the local energy density must be positive somewhere. This result extends to other topologies, but only for certain types of vacuum; in particular, for a generic toroidal boundary, the vacuum’s bulk dual must be the zero-temperature limit of a toroidal black hole.
Issue Date: 19-Oct-2016
Date of Acceptance: 1-Sep-2016
URI: http://hdl.handle.net/10044/1/40666
DOI: https://dx.doi.org/10.1088/0264-9381/33/22/225003
ISSN: 1361-6382
Publisher: IOP Publishing
Journal / Book Title: Classical and Quantum Gravity
Volume: 33
Issue: 22
Copyright Statement: © 2016 IOP Publishing Ltd. This article was published in Classical and Quantum Gravity, 2016, Vol: 33, no. 22.
Keywords: Science & Technology
Physical Sciences
Astronomy & Astrophysics
Physics, Multidisciplinary
Physics, Particles & Fields
Physics
black holes
CFT
energy density
AdS/CFT
MEAN-CURVATURE FLOW
GAUGED EXTENDED SUPERGRAVITY
PENROSE INEQUALITY
POSITIVE ENERGY
BLACK-HOLES
RENORMALIZATION
hep-th
gr-qc
Nuclear & Particles Physics
02 Physical Sciences
01 Mathematical Sciences
Publication Status: Published
Article Number: 225003
Appears in Collections:Physics
Theoretical Physics
Faculty of Natural Sciences



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