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A covariant holographic entanglement entropy proposal

Hubeny, V.E.; Rangamani, M.; Takayanagi, T.

Authors

V.E. Hubeny

M. Rangamani

T. Takayanagi



Abstract

With an aim towards understanding the time-dependence of entanglement entropy in generic quantum field theories, we propose a covariant generalization of the holographic entanglement entropy proposal of hep-th/0603001. Apart from providing several examples of possible covariant generalizations, we study a particular construction based on light-sheets, motivated in similar spirit to the covariant entropy bound underlying the holographic principle. In particular, we argue that the entanglement entropy associated with a specified region on the boundary in the context of the AdS/CFT correspondence is given by the area of a co-dimension two bulk surface with vanishing expansions of null geodesics. We demonstrate our construction with several examples to illustrate its reduction to the holographic entanglement entropy proposal in static spacetimes. We further show how this proposal may be used to understand the time evolution of entanglement entropy in a time varying QFT state dual to a collapsing black hole background. Finally, we use our proposal to argue that the Euclidean wormhole geometries with multiple boundaries should be regarded as states in a non-interacting but entangled set of QFTs, one associated to each boundary.

Citation

Hubeny, V., Rangamani, M., & Takayanagi, T. (2007). A covariant holographic entanglement entropy proposal. Journal of High Energy Physics, 2007(07), https://doi.org/10.1088/1126-6708/2007/07/062

Journal Article Type Article
Publication Date Jul 23, 2007
Deposit Date Jul 23, 2007
Publicly Available Date Mar 29, 2024
Journal Journal of High Energy Physics
Print ISSN 1126-6708
Electronic ISSN 1029-8479
Publisher Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed Peer Reviewed
Volume 2007
Issue 07
DOI https://doi.org/10.1088/1126-6708/2007/07/062
Keywords AdS-CFT Correspondence, Gauge-gravity correspondence.

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