Noncommutativity and Holographic Entanglement Entropy

TL;DR

This paper investigates how noncommutativity in a large N gauge theory affects holographic entanglement entropy, revealing increased divergence and providing insights into geometric contributions in different configurations.

Contribution

It analyzes the impact of noncommutativity on holographic entanglement entropy using the RT-formula in specific geometries, highlighting divergence issues.

Findings

Divergence of entanglement entropy worsens with noncommutativity.

Noncommutativity influences entanglement entropy in rectangular and cylindrical geometries.

Future work includes higher-dimensional theories and black hole backgrounds.

Abstract

In this paper we study the holographic entanglement entropy in a large N noncommutative gauge field theory with two $\theta$ parameters by Ryu-Takayanagi prescription (RT-formula). We discuss what contributions the presence of noncommutativity will make to the entanglement entropy in two different circumstances: 1) a rectangular strip and 2) a cylinder. Since we want to investigate the entanglement entropy only, we will not be discussing the finite temperature case in which the entropy calculated by the area of minimal surface will largely be the thermal part rather than the entanglement part. We find that divergence of the holographic entanglement entropy will be worse in the presence of noncommutativity. In future study, we are going to explore the concrete way of computing holographic entanglement entropy in higher dimensional field theory and investigate more about the entanglement entropy in the presence of black holes/black branes.