The Influence of Angular Momentum and Chemical Potential on Holographic Entanglement Entropy

TL;DR

This paper investigates how angular momentum and chemical potential affect entanglement entropy in a strongly coupled conformal field theory using holographic duality, revealing behaviors in small and large region limits.

Contribution

It provides a detailed analysis of entanglement entropy in rotating charged black hole backgrounds, highlighting the influence of mass, charge, and rotation parameters.

Findings

In the small R limit, entropy depends mainly on mass and rotation.

In the large R limit, extremal surface area approaches the event horizon area.

Entanglement entropy equals the Bekenstein-Hawking entropy for the entire region.

Abstract

We study the entanglement entropy between a strip region with width $2R$ and its complement in strongly coupled large-$N$ conformal field theory (CFT) on $\mathbb{R}^{1,n}$ with chemical potential and angular momentum in an thermal equilibrium state, which dual to the cylindrical Kerr-Newman black hole. Using Ryu-Takanayagi conjecture, we are able to explore the entanglement entropy through calculating the area of the extremal surface which is anchored on the entangled surface. Because we consider the rotating charged black hole for the gravitational dual, the entropy can be characterized by the mass $m$, charge $q$ and rotation $a$ parameters. We find that in the small $R$ limit, only the mass $m$ and the rotation $a$ parameters come in the leading behavior, the quadratic of $R$ term, after subtracting the entanglement entropy in vacuum. In the large $R$ limit, the area of the extremal surface is very close to the area of the event horizon after regularization. When we take the whole spatial region, the entanglement entropy is identical to the thermal entropy, i.e. the Bekenstein-Hawking entropy.