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Title of Journal: J High Energ Phys

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Abbravation: Journal of High Energy Physics

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Springer Berlin Heidelberg

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DOI

10.1007/s11896-016-9198-5

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1029-8479

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Shape dependence of entanglement entropy in confor

Authors: Thomas Faulkner Robert G Leigh Onkar Parrikar
Publish Date: 2016/04/14
Volume: 2016, Issue: 4, Pages: 88-
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Abstract

We study universal features in the shape dependence of entanglement entropy in the vacuum state of a conformal field theory CFT on mathrmmathbbR1d1 We consider the entanglement entropy across a deformed planar or spherical entangling surface in terms of a perturbative expansion in the infinitesimal shape deformation In particular we focus on the second order term in this expansion known as the entanglement density This quantity is known to be nonpositive by the strongsubadditivity property We show from a purely field theory calculation that the nonlocal part of the entanglement density in any CFT is universal and proportional to the coefficient C T appearing in the twopoint function of stress tensors in that CFT As applications of our result we prove the conjectured universality of the corner term coefficient fracsigma C T=fracpi224 in d = 3 CFTs and the holographic Mezei formula for entanglement entropy across deformed spheresThis article is published under an open access license Please check the Copyright Information section for details of this license and what reuse is permitted If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and reuse information please contact the Rights and Permissions team

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