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Title: The gravity duals of modular Hamiltonians

Abstract

In this study, we investigate modular Hamiltonians defined with respect to arbitrary spatial regions in quantum field theory states which have semi-classical gravity duals. We find prescriptions in the gravity dual for calculating the action of the modular Hamiltonian on its defining state, including its dual metric, and also on small excitations around the state. Curiously, use of the covariant holographic entanglement entropy formula leads us to the conclusion that the modular Hamiltonian, which in the quantum field theory acts only in the causal completion of the region, does not commute with bulk operators whose entire gauge-invariant description is space-like to the causal completion of the region.

Authors:
 [1];  [2]
  1. Harvard Univ., Cambridge, MA (United States)
  2. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Publication Date:
Research Org.:
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1362133
Grant/Contract Number:  
SC0012567
Resource Type:
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: 9; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AdS-CFT correspondence; field theories in higher dimensions

Citation Formats

Jafferis, Daniel L., and Suh, S. Josephine. The gravity duals of modular Hamiltonians. United States: N. p., 2016. Web. doi:10.1007/JHEP09(2016)068.
Jafferis, Daniel L., & Suh, S. Josephine. The gravity duals of modular Hamiltonians. United States. doi:10.1007/JHEP09(2016)068.
Jafferis, Daniel L., and Suh, S. Josephine. Mon . "The gravity duals of modular Hamiltonians". United States. doi:10.1007/JHEP09(2016)068. https://www.osti.gov/servlets/purl/1362133.
@article{osti_1362133,
title = {The gravity duals of modular Hamiltonians},
author = {Jafferis, Daniel L. and Suh, S. Josephine},
abstractNote = {In this study, we investigate modular Hamiltonians defined with respect to arbitrary spatial regions in quantum field theory states which have semi-classical gravity duals. We find prescriptions in the gravity dual for calculating the action of the modular Hamiltonian on its defining state, including its dual metric, and also on small excitations around the state. Curiously, use of the covariant holographic entanglement entropy formula leads us to the conclusion that the modular Hamiltonian, which in the quantum field theory acts only in the causal completion of the region, does not commute with bulk operators whose entire gauge-invariant description is space-like to the causal completion of the region.},
doi = {10.1007/JHEP09(2016)068},
journal = {Journal of High Energy Physics (Online)},
number = 9,
volume = 2016,
place = {United States},
year = {2016},
month = {9}
}

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