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Topological aspects of generalized gravitational entropy

Haehl, Felix M.; Hartman, Thomas; Marolf, Donald; Maxfield, Henry; Rangamani, Mukund

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Felix M. Haehl

Thomas Hartman

Donald Marolf

Henry Maxfield

Mukund Rangamani


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 q but not others, along with some other issues


Haehl, F. M., Hartman, T., Marolf, D., Maxfield, H., & Rangamani, M. (2015). Topological aspects of generalized gravitational entropy. Journal of High Energy Physics, 2015(5), Article 23.

Journal Article Type Article
Acceptance Date Apr 14, 2015
Online Publication Date May 30, 2015
Publication Date May 31, 2015
Deposit Date Apr 23, 2019
Publicly Available Date Apr 23, 2019
Journal Journal of High Energy Physics
Print ISSN 1126-6708
Publisher Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed Peer Reviewed
Volume 2015
Issue 5
Article Number 23


Published Journal Article (706 Kb)

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Copyright Statement
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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