Topological aspects of generalized gravitational entropy

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

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 q but not others, along with some other issues

Citation

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. https://doi.org/10.1007/jhep05%282015%29023

• 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
• DOI: https://doi.org/10.1007/jhep05%282015%29023