Modular Hamiltonians for deformed half-spaces and the averaged null energy condition
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Publication:1639164
DOI10.1007/JHEP09(2016)038zbMATH Open1390.83106arXiv1605.08072WikidataQ114232649 ScholiaQ114232649MaRDI QIDQ1639164
Author name not available (Why is that?)
Publication date: 12 June 2018
Published in: (Search for Journal in Brave)
Abstract: We study modular Hamiltonians corresponding to the vacuum state for deformed half-spaces in relativistic quantum field theories on . 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. These 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. We also discuss the AdS/CFT counterpart of this result, making connection with the recently proposed gravitational dual for modular Hamiltonians in holographic theories.
Full work available at URL: https://arxiv.org/abs/1605.08072
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