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Journal of High Energy Physics

, 2014:162 | Cite as

Causality & holographic entanglement entropy

  • Matthew Headrick
  • Veronika E. Hubeny
  • Albion Lawrence
  • Mukund Rangamani
Open Access
Regular Article - Theoretical Physics

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.

Keywords

AdS-CFT Correspondence Classical Theories of Gravity 

Notes

Open Access

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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Copyright information

© The Author(s) 2014

Authors and Affiliations

  • Matthew Headrick
    • 1
  • Veronika E. Hubeny
    • 2
  • Albion Lawrence
    • 1
  • Mukund Rangamani
    • 2
  1. 1.Martin Fisher School of PhysicsBrandeis UniversityWalthamU.S.A.
  2. 2.Centre for Particle Theory & Department of Mathematical SciencesScience LaboratoriesDurhamU.K.

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