Rényi entropy and conformal defects

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.

37 pages, typos corrected, section 6 and appendix C expanded, references added

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• Shape Dependence of Holographic Rényi Entropy in General Dimensions
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• Spinning conformal defects
• Comments on Squashed-sphere Partition Functions
• Universality for Shape Dependence of Casimir Effects from Weyl Anomaly
• Universality in the Shape Dependence of Holographic Rényi Entropy for General Higher Derivative Gravity
• Generalizing the entanglement entropy of singular regions in conformal field theories
• Surface operators in the 6d $\mathcal{N}=(2,0)$ theory
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• Operator product expansion for conformal defects
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• Radiation, entanglement and islands from a boundary local quench
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