Supersymmetric R\'enyi Entropy and Defect Operators

TL;DR

This paper interprets supersymmetric R'enyi entropies in superconformal field theories as expectation values of defect operators, computed exactly via localization, revealing a relationship between partition functions on different geometries.

Contribution

It introduces a defect operator perspective for supersymmetric R'enyi entropies and computes their expectation values exactly using localization techniques.

Findings

Exact expectation values of defect operators match supersymmetric R'enyi entropies.

Establishes a relationship between partition functions on squashed and round spheres with defects.

Provides a unified framework for understanding entropies in superconformal theories.

Abstract

We describe the defect operator interpretation of the supersymmetric Renyi entropies of superconformal field theories in three, four and five dimensions. The operators involved are supersymmetric codimension-two defects in an auxiliary Z_n gauge theory coupled to n copies of the SCFT. We compute the exact expectation values of such operators using localization, and compare the results to the supersymmetric Renyi entropy. The agreement between the two implies a relationship between the partition function on a squashed sphere and the one on a round sphere in the presence of defects.