Causality & holographic entanglement entropy

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

doi:10.1007/JHEP12(2014)162

Title: Causality & holographic entanglement entropy

Journal Article · Mon Dec 29 00:00:00 EST 2014 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP12(2014)162· OSTI ID:1454767

Headrick, Matthew ^[1]; Hubeny, Veronika E. ^[2]; Lawrence, Albion ^[1]; Rangamani, Mukund ^[2]

Brandeis Univ., Waltham, MA (United States). Martin Fisher School of Physics
Science Laboratories, Durham (United Kingdom). Centre for Particle Theory & Department of Mathematical Sciences

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.

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Research Organization:: Brandeis Univ., Waltham, MA (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0009987

OSTI ID:: 1454767

Journal Information:: Journal of High Energy Physics (Online), Vol. 2014, Issue 12; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 242 works

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