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Entanglement entropy in three dimensional gravity

Maxfield, Henry

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Henry Maxfield


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.


Maxfield, H. (2015). Entanglement entropy in three dimensional gravity. Journal of High Energy Physics, 2015(4), Article 31.

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
Public URL


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