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Title: Relative entropy equals bulk relative entropy

We consider the gravity dual of the modular Hamiltonian associated to a general subregion of a boundary theory. We use it to argue that the relative entropy of nearby states is given by the relative entropy in the bulk, to leading order in the bulk gravitational coupling. We also argue that the boundary modular flow is dual to the bulk modular flow in the entanglement wedge, with implications for entanglement wedge reconstruction.
 [1] ;  [2] ;  [3] ;  [4]
  1. Harvard Univ., Cambridge, MA (United States). Center for Fundamental Laws of Nature
  2. Princeton Univ., NJ (United States)
  3. Inst. for Advanced Study, Princeton, NJ (United States)
  4. Kavli Inst. for Theoretical Physics, Santa Barbara, CA (United States); Univ. of British Columbia, Vancouver, BC (Canada). Dept. of Physics and Astronomy
Publication Date:
OSTI Identifier:
Grant/Contract Number:
SC0009988; PHY-1352084; PHY-1314198; PHY11-25915; 376206
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 6; Journal ID: ISSN 1029-8479
Springer Berlin
Research Org:
Inst. for Advanced Study, Princeton, NJ (United States)
Sponsoring Org:
USDOE; USNSF; Natural Sciences and Engineering Research Council of Canada; Simons Foundation
Country of Publication:
United States
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS AdS-CFT Correspondence; 1/N Expansion, Models of Quantum Gravity; Field Theories in Higher Dimensions