Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 12, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP12(2014)162
Keywords
AdS-CFT Correspondence; Classical Theories of Gravity
Categories
Funding
- National Science Foundation [1066293, PHY10-53842]
- Ambrose Monell foundation
- FQXi grant Measures of Holographic Information [FQXi-RFP3-1334]
- STFC Consolidated Grant [ST/J000426/1]
- DOE [DE-SC0009987]
- European Research Council under the European Union's Seventh Framework Programme (FP7)
- ERC Consolidator Grant Agreement [ERC-2013-CoG-615443]
- STFC [ST/J000426/1, ST/L000407/1] Funding Source: UKRI
- Division Of Physics
- Direct For Mathematical & Physical Scien [1053842] Funding Source: National Science Foundation
- Science and Technology Facilities Council [ST/J000426/1, ST/L000407/1] Funding Source: researchfish
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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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