Supersymmetric Renyi Entropy in $CF{T}_2$ and $Ad{S}_3$

Abstract

We show that in any two dimensional conformal field theory with (2, 2) supersymmetry one can define a supersymmetric analog of the usual Renyi entropy of a spatial region A. It differs from the Renyi entropy by a universal function (which we compute) of the central charge, Renyi parameter n and the geometric parameters of A. In the limit $n\to 1$ it coincides with the entanglement entropy. Thus, it contains the same information as the Renyi entropy but its computation only involves correlation functions of chiral and anti-chiral operators. We also show that this quantity appears naturally in string theory on $Ad{S}_3$.

15 pages; v2: reference added

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