Rényi entropy and conformal defects
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Publication:1638924
DOI10.1007/JHEP07(2016)076zbMATH Open1390.81486arXiv1511.06713OpenAlexW2285145703MaRDI QIDQ1638924
Author name not available (Why is that?)
Publication date: 12 June 2018
Published in: (Search for Journal in Brave)
Abstract: We propose a field theoretic framework for calculating the dependence of R'enyi entropies on the shape of the entangling surface in a conformal field theory. Our approach rests on regarding the corresponding twist operator as a conformal defect and in particular, we define the displacement operator which implements small local deformations of the entangling surface. We identify a simple constraint between the coefficient defining the two-point function of the displacement operator and the conformal weight of the twist operator, which consolidates a number of distinct conjectures on the shape dependence of the R'enyi entropy. As an example, using this approach, we examine a conjecture regarding the universal coefficient associated with a conical singularity in the entangling surface for CFTs in any number of spacetime dimensions. We also provide a general formula for the second order variation of the R'enyi entropy arising from small deformations of a spherical entangling surface, extending Mezei's results for the entanglement entropy.
Full work available at URL: https://arxiv.org/abs/1511.06713
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