Supersymmetric Rényi Entropy in Five Dimensions

TL;DR

This work extends the concept of supersymmetric Rényi entropy to ${\cal N}=1$ five-dimensional gauge theories and derives a matrix-model representation via localization on the n-covering of S^5. In the large-N limit, the authors obtain explicit expressions for the SUSY Rényi entropy and its Wilson-loop variation, and show exact agreement with a gravity dual constructed in Romans F(4) supergravity as a supersymmetric charged topological AdS6 black hole. The gravity analysis also yields a holographic Wilson loop result that matches the field-theory computation, reinforcing the AdS/CFT correspondence in this higher-dimensional setting. Overall, the paper provides a concrete higher-dimensional realization of SUSY Rényi entropy, connecting field-theoretic localization, large-N dynamics, and holographic duality with and without Wilson-loop insertions.

Abstract

We introduce supersymmetric Rényi 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 Rényi 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.