Causality & Holographic Entanglement Entropy

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

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
• Electronic ISSN: 1029-8479
• 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.
• Public URL: https://durham-repository.worktribe.com/output/1417661