Entanglement entropy of Wilson loops: Holography and matrix models

TL;DR

This paper compares holographic and matrix model calculations of entanglement entropy for Wilson loops in N=4 supersymmetric Yang-Mills theory, finding perfect agreement and advancing understanding of gauge/gravity duality.

Contribution

It demonstrates the equivalence of holographic and matrix model approaches to entanglement entropy for Wilson loops in a specific supersymmetric gauge theory.

Findings

Holographic and matrix model results for entanglement entropy agree perfectly.

The study extends the understanding of entanglement entropy in gauge/gravity duality.

Provides a new holographic calculation matching matrix model predictions.

Abstract

A half-BPS circular Wilson loop in $\mathcal{N}=4$ $SU(N)$ supersymmetric Yang-Mills theory in an arbitrary representation is described by a Gaussian matrix model with a particular insertion. The additional entanglement entropy of a spherical region in the presence of such a loop was recently computed by Lewkowycz and Maldacena using exact matrix model results. In this note we utilize the supergravity solutions that are dual to such Wilson loops in a representation with order $N^2$ boxes to calculate this entropy holographically. Employing the matrix model results of Gomis, Matsuura, Okuda and Trancanelli we express this holographic entanglement entropy in a form that can be compared with the calculation of Lewkowycz and Maldacena. We find complete agreement between the matrix model and holographic calculations.