Supersymmetric R\'enyi entropy and charged hyperbolic black holes

TL;DR

This paper establishes a precise holographic correspondence between supersymmetric R'enyi entropy in SCFTs with flavor defects and charged hyperbolic black holes in supergravity, verified through exact calculations and matching results.

Contribution

It provides the first exact holographic computation of supersymmetric R'enyi entropy for SCFTs with flavor defects using charged hyperbolic black holes.

Findings

Exact match between field theory and gravity calculations of R'enyi entropy.

Established a direct map between field theory chemical potentials and gravity parameters.

Extended the analysis to include cases with angular momentum.

Abstract

The supersymmetric R\'enyi entropy across a spherical entangling surface in a $d$-dimensional SCFT with flavor defects is equivalent to a supersymmetric partition function on $\mathbb{H}^{d-1} \times \mathbb{S}^1$, which can be computed exactly using localization. We consider the holographically dual BPS solutions in $(d +1)$-dimensional matter coupled supergravity $(d = 3 , 5)$, which are charged hyperbolically sliced AdS black holes. We compute the renormalized on-shell action and the holographic supersymmetric R\'enyi entropy and show a perfect match with the field theory side. Our setup allows a direct map between the chemical potentials for the global symmetries of the field theories and those of the gravity solutions. We also discuss a simple case where angular momentum is added.