Holographic calculations of R\'enyi entropy from rotating topological black holes

TL;DR

This paper introduces a new holographic entanglement measure called rotating Rnyi entropy, calculated from rotating topological black holes, revealing its dependence on chemical potential and replica parameters in the dual CFT.

Contribution

The paper constructs a novel holographic entanglement measure based on rotating topological black holes and explores its properties in the dual conformal field theory.

Findings

Rotating Rnyi entropy can be computed holographically from topological black holes.

The entropy depends on the black hole's angular velocity, temperature, and chemical potential.

Behavior of the generalized Rnyi entropy with respect to these parameters is characterized.

Abstract

We construct a new class of entanglement measures named "rotating R\'enyi entropy" by the holographic calculation of a rotating topological black hole belonging to the Petrov type-D class, we compute this kind of entropy for a spherical entangling surface of a vacuum state in the dual CFT. We find that the latter one could be conformally transformed to a thermal state on the boundary geometry of the rotating topological black hole with certain temperature. Then according to the angular velocity of the bulk black hole, we introduce the chemical potential in the boundary thermodynamics, which appears in the definition of the generalized R\'enyi entropy, and we presented the behaviors of this generalized R\'enyi entropy with the chemical potential and replica parameters.