The holographic supersymmetric Renyi entropy in five dimensions

TL;DR

This work computes the supersymmetric Renyi entropy across an entangling $S^3$ in five-dimensional SCFTs using localization and a conformal mapping to a squashed $S^5$. For a class of USp$(2N)$ theories, the authors derive a large-$N$ free-energy scaling $F_n=\frac{(1+2n)^3}{27n^2}F_{S^5,\mathrm{round}}$, yielding a Renyi entropy $S_n= -\frac{1+7n+19n^2}{27n^2}F_{S^5,\mathrm{round}}$, and show that the partition function reduces to a squashed-sphere background with parameters $(b_1,b_2,b_3)=(1,1,1/n)$. On the holographic side, a 1/2-BPS Euclidean black hole in Euclidean Romans $F(4)$ supergravity is constructed, globally regular, and its on-shell free energy reproduces the field-theory result; a fundamental-string dual gives a Wilson loop scaling $\log\langle W\rangle_n=\frac{1+2n}{3}\log\langle W\rangle_{n=1}$. Overall, the results support a general holographic formula for the free energy in terms of the squashing parameters, $F=\frac{(|b_1|+|b_2|+|b_3|)^3}{27|b_1b_2b_3|}F_{\mathrm{AdS}_6}$, and demonstrate consistency between localization, squashed-sphere physics, and AdS$_6$ holography in this 5D setting.

Abstract

We compute the supersymmetric Renyi entropy across an entangling three-sphere for five-dimensional superconformal field theories using localization. For a class of USp(2N) gauge theories we construct a holographic dual 1/2 BPS black hole solution of Euclidean Romans F(4) supergravity. The large N limit of the gauge theory results agree perfectly with the supergravity computations.