Modular Hamiltonians for deformed half-spaces and the averaged null energy condition
Abstract
We study modular Hamiltonians corresponding to the vacuum state for deformed half-spaces in relativistic quantum field theories on R1,d-1. We show that in addition to the usual boost generator, there is a contribution to the modular Hamiltonian at first order in the shape deformation, proportional to the integral of the null components of the stress tensor along the Rindler horizon. We use this fact along with monotonicity of relative entropy to prove the averaged null energy condition in Minkowski space-time. This subsequently gives a new proof of the Hofman-Maldacena bounds on the parameters appearing in CFT three-point functions. Our main technical advance involves adapting newly developed perturbative methods for calculating entanglement entropy to the problem at hand. Our methods were recently used to prove certain results on the shape dependence of entanglement in CFTs and here we generalize these results to excited states and real time dynamics. Finally, we discuss the AdS/CFT counterpart of this result, making connection with the recently proposed gravitational dual for modular Hamiltonians in holographic theories.
- Authors:
-
- Univ. of Illinois, Urbana, IL (United States). Dept. of Physics
- Publication Date:
- Research Org.:
- Univ. of Illinois at Urbana-Champaign, IL (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1395542
- Grant/Contract Number:
- FG02-13ER42001; SC0009932
- 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
Faulkner, Thomas, Leigh, Robert G., Parrikar, Onkar, and Wang, Huajia. Modular Hamiltonians for deformed half-spaces and the averaged null energy condition. United States: N. p., 2016.
Web. doi:10.1007/JHEP09(2016)038.
Faulkner, Thomas, Leigh, Robert G., Parrikar, Onkar, & Wang, Huajia. Modular Hamiltonians for deformed half-spaces and the averaged null energy condition. United States. https://doi.org/10.1007/JHEP09(2016)038
Faulkner, Thomas, Leigh, Robert G., Parrikar, Onkar, and Wang, Huajia. Thu .
"Modular Hamiltonians for deformed half-spaces and the averaged null energy condition". United States. https://doi.org/10.1007/JHEP09(2016)038. https://www.osti.gov/servlets/purl/1395542.
@article{osti_1395542,
title = {Modular Hamiltonians for deformed half-spaces and the averaged null energy condition},
author = {Faulkner, Thomas and Leigh, Robert G. and Parrikar, Onkar and Wang, Huajia},
abstractNote = {We study modular Hamiltonians corresponding to the vacuum state for deformed half-spaces in relativistic quantum field theories on R1,d-1. We show that in addition to the usual boost generator, there is a contribution to the modular Hamiltonian at first order in the shape deformation, proportional to the integral of the null components of the stress tensor along the Rindler horizon. We use this fact along with monotonicity of relative entropy to prove the averaged null energy condition in Minkowski space-time. This subsequently gives a new proof of the Hofman-Maldacena bounds on the parameters appearing in CFT three-point functions. Our main technical advance involves adapting newly developed perturbative methods for calculating entanglement entropy to the problem at hand. Our methods were recently used to prove certain results on the shape dependence of entanglement in CFTs and here we generalize these results to excited states and real time dynamics. Finally, we discuss the AdS/CFT counterpart of this result, making connection with the recently proposed gravitational dual for modular Hamiltonians in holographic theories.},
doi = {10.1007/JHEP09(2016)038},
journal = {Journal of High Energy Physics (Online)},
number = 9,
volume = 2016,
place = {United States},
year = {Thu Sep 08 00:00:00 EDT 2016},
month = {Thu Sep 08 00:00:00 EDT 2016}
}
Web of Science
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