Supersymmetric Renyi Entropy in $CFT_2$ and $AdS_3$

TL;DR

This paper introduces a supersymmetric version of Renyi entropy in 2D superconformal field theories, computes its universal form, and relates it to string theory on AdS3, providing a new tool for understanding entanglement in supersymmetric systems.

Contribution

It defines and computes a supersymmetric Renyi entropy in 2D (2,2) SCFTs, linking it to string theory on AdS3 and simplifying calculations via chiral correlation functions.

Findings

Supersymmetric Renyi entropy differs from standard by a universal function.

In the limit n→1, it reduces to supersymmetric entanglement entropy.

The quantity naturally appears in string theory on AdS3.

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 $n \to1$ 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 $AdS_3$.