Supersymmetric R\'enyi Entropy in Five Dimensions

TL;DR

This paper defines supersymmetric R'enyi entropies for 5D gauge theories, computes their large-N behavior via localization, and confirms the results through gravity duals involving supersymmetric black holes, including Wilson loop effects.

Contribution

It introduces a new supersymmetric R'enyi entropy framework for five-dimensional theories and demonstrates agreement with gravity dual calculations.

Findings

Large-N behavior matches gravity dual predictions

Wilson loop insertions affect R'enyi entropy as computed from both sides

Localization method effectively computes supersymmetric entropies in 5D

Abstract

We introduce supersymmetric R\'enyi entropies for $\mathcal{N}=1$ supersymmetric gauge theories in five dimensions. The matrix model representation is obtained using the localization method and the large-$N$ behavior is studied. The gravity dual is a supersymmetric charged topological AdS$_6$ black hole in the Romans $F(4)$ supergravity. The variation of the supersymmetric R\'enyi entropy due to the insertion of a BPS Wilson loop is computed. We find perfect agreements between the large-$N$ and the dual gravity computations both with and without the Wilson loop operator.