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Causality & Holographic Entanglement Entropy

Headrick, Matthew; Hubeny, Veronika E.; Lawrence, Albion; Rangamani, Mukund

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Authors

Matthew Headrick

Veronika E. Hubeny

Albion Lawrence

Mukund Rangamani



Abstract

We identify conditions for the entanglement entropy as a function of spatial region to be compatible with causality in an arbitrary relativistic quantum field theory. We then prove that the covariant holographic entanglement entropy prescription (which relates entanglement entropy of a given spatial region on the boundary to the area of a certain extremal surface in the bulk) obeys these conditions, as long as the bulk obeys the null energy condition. While necessary for the validity of the prescription, this consistency requirement is quite nontrivial from the bulk standpoint, and therefore provides important additional evidence for the prescription. In the process, we introduce a codimension-zero bulk region, named the entanglement wedge, naturally associated with the given boundary spatial region. We propose that the entanglement wedge is the most natural bulk region corresponding to the boundary reduced density matrix.

Citation

Headrick, M., Hubeny, V. E., Lawrence, A., & Rangamani, M. (2014). Causality & Holographic Entanglement Entropy. Journal of High Energy Physics, 2014(12), Article 162. https://doi.org/10.1007/jhep12%282014%29162

Journal Article Type Article
Acceptance Date Dec 7, 2014
Online Publication Date Dec 29, 2014
Publication Date Dec 29, 2014
Deposit Date Dec 19, 2014
Publicly Available Date Jan 8, 2015
Journal Journal of High Energy Physics
Print ISSN 1126-6708
Publisher Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed Peer Reviewed
Volume 2014
Issue 12
Article Number 162
DOI https://doi.org/10.1007/jhep12%282014%29162
Keywords AdS-CFT correspondence, Entanglement entropy.

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Publisher Licence URL
http://creativecommons.org/licenses/by/4.0/

Copyright Statement
© 2014 The Authors. 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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