Holographic R\'enyi entropy for two-dimensional $\mathcal{N}$=(2,2) superconformal field theory

TL;DR

This paper computes the holographic Re9nyi entropy for 2D a9(2,2) superconformal field theories, matching results from supergravity and SCFT calculations for intervals on complex plane and torus.

Contribution

It provides the first detailed comparison of Re9nyi entropy calculations between supergravity and a9(2,2) SCFT, including mutual information and entropy expansions.

Findings

Re9nyi mutual information expanded to order x^4

Re9nyi entropy on torus expanded to order q^2

Results from supergravity and SCFT match

Abstract

We investigate the holographic R\'enyi entropy for two-dimensional $\mathcal N=(2,2)$ superconformal field theory (SCFT), which is dual to $\mathcal N=2$ supergravity in AdS$_3$ background. In SCFT we have the stress tensor, current, and their supersymmetric partners, and in supergravity we have the graviton, vector field, and two gravitinos. We get the R\'enyi mutual information of two short intervals on complex plane in expansion by the cross ratio $x$ to order $x^4$, and R\'enyi entropy of one interval on torus in expansion by $q=\exp(-2\pi\beta/L)$, with $\beta$ being the inverse temperature and $L$ being the spatial period, to order $q^2$. We calculate in both the supergravity and SCFT sides, and find matches of the results.