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arXiv · 1511.06713

Rényi entropy and conformal defects

Lorenzo Bianchi·Marco Meineri·Robert C. Myers·Michael Smolkin
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Abstract

We propose a field theoretic framework for calculating the dependence of Rényi 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 Rényi 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 Rényi entropy arising from small deformations of a spherical entangling surface, extending Mezei's results for the entanglement entropy.

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Lorenzo Bianchi, Marco Meineri, Robert C. Myers, Michael Smolkin. 2016-04-18. Rényi entropy and conformal defects. https://doi.org/10.1007/jhep07(2016)076

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