Extending Charged Holographic R\'enyi Entropy

TL;DR

This paper generalizes the charged holographic R'enyi entropy by incorporating pressure variations of charged AdS black holes, revealing new interactions and providing a field theoretic interpretation, especially in two dimensions.

Contribution

It introduces an extended charged R'enyi entropy framework that includes pressure effects, offering new insights into holographic entanglement and black hole thermodynamics.

Findings

Identified an interplay between black hole pressure and charge in R'enyi entropy.

Provided a field theory interpretation using twist operators in 2D.

Formulated an area law for the extended R'enyi entropy.

Abstract

Motivated by extended black hole thermodynamics, we generalize the R\'enyi entropy of charged holographic conformal field theories (CFTs) in $d$-dimensions. Specifically, following (1807.09215), we extend the quench description of the R\'enyi entropy of globally charged holographic CFTs by including pressure variations of charged hyperbolically sliced anti de Sitter black holes. We provide an exhaustive analysis of the new type of charged R\'enyi entropy, where we find an interesting interplay between a parameter controlling the pressure of the black hole and its charge. A field theoretic interpretation of this extended charged R\'enyi entropy is given. In particular, in $d=2$, where the bulk geometry becomes the charged Ba\~nados, Teitelboim, Zanelli black hole, we write down the extended charged R\'enyi entropy in terms of the twist operators of the charged field theory. An area law prescription for the extended R\'enyi entropy is formulated. We comment on several avenues for future work, including how global charge conservation relates to black hole super-entropicity.