Entanglement entropy in three dimensional gravity

Maxfield, Henry

Abstract

The Ryu-Takayanagi (RT) and covariant Hubeny-Rangamani-Takayanagi (HRT) proposals relate entanglement entropy in CFTs with holographic duals to the areas of minimal or extremal surfaces in the bulk geometry. We show how, in three dimensional pure gravity, the relevant regulated geodesic lengths can be obtained by writing a spacetime as a quotient of AdS3, with the problem reduced to a simple purely algebraic calculation. We explain how this works in both Lorentzian and Euclidean formalisms, before illustrating its use to obtain novel results in a number of examples, including rotating BTZ, the R P 2 RP2 geon, and several wormhole geometries. This includes spatial and temporal dependence of single-interval entanglement entropy, despite these symmetries being broken only behind an event horizon. We also discuss considerations allowing HRT to be derived from analytic continuation of Euclidean computations in certain contexts, and a related class of complexified extremal surfaces.

• Journal Article Type: Article
• Acceptance Date: Mar 16, 2015
• Online Publication Date: Apr 7, 2015
• Publication Date: Apr 7, 2015
• Deposit Date: Apr 9, 2019
• Publicly Available Date: Apr 10, 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: 4
• Article Number: 31
• DOI: https://doi.org/10.1007/jhep04%282015%29031
• Public URL: https://durham-repository.worktribe.com/output/1333519