Holographic Entanglement in a Noncommutative Gauge Theory

TL;DR

This paper explores entanglement entropy and mutual information in a noncommutative gauge theory using holographic duality, revealing unique behaviors and the necessity of a cutoff in the noncommutative plane.

Contribution

It introduces a scheme for defining spatial regions in noncommutative geometries and computes entanglement entropy using the Ryu-Takayanagi prescription, highlighting peculiar properties.

Findings

Entanglement entropy depends on the region’s orientation relative to the noncommutative plane.

A cutoff is essential to handle divergences in entanglement entropy.

Regions entirely in the noncommutative plane exhibit unique minimal surface properties.

Abstract

In this article we investigate aspects of entanglement entropy and mutual information in a large-N strongly coupled noncommutative gauge theory, both at zero and at finite temperature. Using the gauge-gravity duality and the Ryu-Takayanagi (RT) prescription, we adopt a scheme for defining spatial regions on such noncommutative geometries and subsequently compute the corresponding entanglement entropy. We observe that for regions which do not lie entirely in the noncommutative plane, the RT-prescription yields sensible results. In order to make sense of the divergence structure of the corresponding entanglement entropy, it is essential to introduce an additional cut-off in the theory. For regions which lie entirely in the noncommutative plane, the corresponding minimal area surfaces can only be defined at this cut-off and they have distinctly peculiar properties.