Shape Deformations of Charged R\'enyi Entropies from Holography

TL;DR

This paper uses holography to analyze how small shape deformations affect charged Re9nyi entropies, revealing a universal coefficient linked to the displacement operator and exploring supersymmetric cases.

Contribution

It introduces a holographic method to compute the shape dependence of charged Re9nyi entropies and relates it to defect operator correlation functions.

Findings

Numerical solutions for various chemical potentials and dimensions.

Analytic expressions near  for small chemical potential.

A conjectured relation in supersymmetric cases.

Abstract

Charged and symmetry-resolved R\'enyi entropies are entanglement measures quantifying the degree of entanglement within different charge sectors of a theory with a conserved global charge. We use holography to determine the dependence of charged R\'enyi entropies on small shape deformations away from a spherical or planar entangling surface in general dimensions. This dependence is completely characterized by a single coefficient appearing in the two point function of the displacement operator associated with the R\'enyi defect. We extract this coefficient using its relation to the one point function of the stress tensor in the presence of a deformed entangling surface. This is mapped to a holographic calculation in the background of a deformed charged black hole with hyperbolic horizon. We obtain numerical solutions for different values of the chemical potential and replica number $n$ in various spacetime dimensions, as well as analytic expressions for small chemical potential near $n=1$. When the R\'enyi defect becomes supersymmetric, we demonstrate a conjectured relation between the two point function of the displacement operator and the conformal weight of the twist operator.