Supersymmetric R\'enyi Entropy in Two Dimensions

TL;DR

This paper calculates the exact supersymmetric R'enyi entropy in two-dimensional theories, revealing it is equivalent to entanglement entropy and interpreting conical singularities as defects on the sphere.

Contribution

It provides an exact localization-based computation showing the independence of supersymmetric R'enyi entropy from the branching parameter in two dimensions.

Findings

Supersymmetric R'enyi entropy equals entanglement entropy in 2D.

Partition function on branched sphere is independent of the parameter q.

Conical singularities are interpreted as defects on the sphere.

Abstract

We compute the exact partition function on the branched two-sphere by the localization technique. It is found that it does not depend on a branching parameter q, which means that supersymmetric R\'enyi entropy defined by utilizing it is equivalent to the usual entanglement entropy. We also provide the interpretation of the conical singularities on the branched sphere as defects sit on the poles of the nonsingular two-sphere.