Modular Hamiltonians for deformed half-spaces and the averaged null energy condition

Faulkner, Thomas; Leigh, Robert G.; Parrikar, Onkar; Wang, Huajia

doi:10.1007/JHEP09(2016)038

Title: Modular Hamiltonians for deformed half-spaces and the averaged null energy condition

Journal Article · Thu Sep 08 04:00:00 UTC 2016 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/JHEP09(2016)038 · OSTI ID:1395542

Faulkner, Thomas ^[1]; Leigh, Robert G. ^[2]; Parrikar, Onkar ^[2]; Wang, Huajia ^[2]

Univ. of Illinois, Urbana, IL (United States). Dept. of Physics; Univ. of Illinois, Urbana, IL (United States), Dept. of Physics
Univ. of Illinois, Urbana, IL (United States). Dept. of Physics

We study modular Hamiltonians corresponding to the vacuum state for deformed half-spaces in relativistic quantum field theories on R^1,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.

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Research Organization:: Univ. of Illinois, Urbana, IL (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0009932; SC0009932

OSTI ID:: 1395542

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 9 Vol. 2016; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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The Conformal Bootstrap: Theory, Numerical Techniques, and Applications Poland, David; Rychkov, Slava; Vichi, Alessandro arXiv https://doi.org/10.48550/arxiv.1805.04405	text	January 2018
A Conformal Collider for Holographic CFTs Afkhami-Jeddi, Nima; Kundu, Sandipan; Tajdini, Amirhossein arXiv https://doi.org/10.48550/arxiv.1805.07393	text	January 2018
A perturbative perspective on self-supporting wormholes Fu, Zicao; Grado-White, Brianna; Marolf, Donald arXiv https://doi.org/10.48550/arxiv.1807.07917	text	January 2018
Bootstrap and collider physics of parity violating conformal field theories in $d=3$ Chowdhury, Subham Dutta; David, Justin R.; Prakash, Shiroman arXiv https://doi.org/10.48550/arxiv.1812.07774	preprint	January 2018
The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole Almheiri, Ahmed; Engelhardt, Netta; Marolf, Donald arXiv https://doi.org/10.48550/arxiv.1905.08762	text	January 2019
Spectrum of Modular Hamiltonian in the Vacuum and Excited States Das, Suchetan; Ezhuthachan, Bobby arXiv https://doi.org/10.48550/arxiv.1906.00726	text	January 2019
The entanglement and relative entropy of a chiral fermion on the torus Fries, Pascal; Reyes, Ignacio A. arXiv https://doi.org/10.48550/arxiv.1906.02207	text	January 2019
The Holographic Dual of the Entanglement Wedge Symplectic Form Kirklin, Josh arXiv https://doi.org/10.48550/arxiv.1910.00457	text	January 2019

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