Analytic critical points of charged Renyi entropies from hyperbolic black holes

TL;DR

This paper analytically investigates phase transitions in charged Renyi entropies within holographic models dual to super-Yang-Mills theory, revealing zero modes indicating instabilities of extremal hyperbolic black holes.

Contribution

It provides an analytical study of zero modes and instabilities in charged hyperbolic black holes, extending previous near-horizon analyses to full retarded Green's functions.

Findings

Identified zero modes signaling phase transitions.

Analytically solved for full retarded Green's functions.

Compared stability of two different black hole systems.

Abstract

We analytically study phase transitions of holographic charged Renyi entropies in two gravitational systems dual to the $\mathcal{N}=4$ super-Yang-Mills theory at finite density and zero temperature. The first system is the Reissner-Nordstrom-AdS$_5$ black hole, which has finite entropy at zero temperature. The second system is a charged dilatonic black hole in AdS$_5$, which has zero entropy at zero temperature. Hyperbolic black holes are employed to calculate the Renyi entropies with the entangling surface being a sphere. We perturb each system by a charged scalar field, and look for a zero mode signaling the instability of the extremal hyperbolic black hole. Zero modes as well as the leading order of the full retarded Green's function are analytically solved for both systems, in contrast to previous studies in which only the IR (near horizon) instability was analytically treated.