Topological aspects of generalized gravitational entropy
Topological aspects of generalized gravitational entropy
The holographic prescription for computing entanglement entropy requires that the bulk extremal surface, whose area encodes the amount of entanglement, satisfies a homology constraint. Usually this is stated as the requirement of a (spacelike) interpolating surface that connects the region of interest and the extremal surface. We investigate to what extent this constraint is upheld by the generalized gravitational entropy argument, which relies on constructing replica symmetric q-fold covering spaces of the bulk, branched at the extremal surface. We prove (at the level of topology) that the putative extremal surface satisfies the homology constraint if and only if the corresponding branched cover can be constructed for every positive integer q. We give simple examples to show that homology can be violated if the cover exists for some values of q but not others, along with some other issues.
hep-th, gr-qc
Haehl, Felix M.
eb0d74fd-0d8b-4b1b-8686-79d43c2a3a5f
Hartman, Thomas
6fa2ed5e-ce13-4c30-8f75-7cfcd789b332
Marolf, Donald
8bf4aa69-1fed-4f8e-906d-816823fcc60b
Maxfield, Henry
2591ccf3-ff34-4688-8ac0-94a8dcf8a861
Rangamani, Mukund
c6e93885-0b7e-4e8c-92e5-56227da78a81
5 May 2015
Haehl, Felix M.
eb0d74fd-0d8b-4b1b-8686-79d43c2a3a5f
Hartman, Thomas
6fa2ed5e-ce13-4c30-8f75-7cfcd789b332
Marolf, Donald
8bf4aa69-1fed-4f8e-906d-816823fcc60b
Maxfield, Henry
2591ccf3-ff34-4688-8ac0-94a8dcf8a861
Rangamani, Mukund
c6e93885-0b7e-4e8c-92e5-56227da78a81
Haehl, Felix M., Hartman, Thomas, Marolf, Donald, Maxfield, Henry and Rangamani, Mukund
(2015)
Topological aspects of generalized gravitational entropy.
Journal of High Energy Physics, [023 (2015)].
(doi:10.1007/JHEP05(2015)023).
Abstract
The holographic prescription for computing entanglement entropy requires that the bulk extremal surface, whose area encodes the amount of entanglement, satisfies a homology constraint. Usually this is stated as the requirement of a (spacelike) interpolating surface that connects the region of interest and the extremal surface. We investigate to what extent this constraint is upheld by the generalized gravitational entropy argument, which relies on constructing replica symmetric q-fold covering spaces of the bulk, branched at the extremal surface. We prove (at the level of topology) that the putative extremal surface satisfies the homology constraint if and only if the corresponding branched cover can be constructed for every positive integer q. We give simple examples to show that homology can be violated if the cover exists for some values of q but not others, along with some other issues.
Text
1412.7561v2
- Accepted Manuscript
Available under License Other.
Text
JHEP05(2015)023
- Version of Record
More information
Submitted date: 23 December 2014
Published date: 5 May 2015
Additional Information:
28 pages, 3 figures. v2: clarifications added. figure updated. matches published version
Keywords:
hep-th, gr-qc
Identifiers
Local EPrints ID: 469966
URI: http://eprints.soton.ac.uk/id/eprint/469966
ISSN: 1126-6708
PURE UUID: b558bf37-307e-4dbb-904e-99431164cdc7
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Date deposited: 29 Sep 2022 16:40
Last modified: 17 Mar 2024 04:14
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Contributors
Author:
Felix M. Haehl
Author:
Thomas Hartman
Author:
Donald Marolf
Author:
Henry Maxfield
Author:
Mukund Rangamani
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