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arXiv · 1407.5629

Entanglement entropy of Wilson loops: Holography and matrix models

Simon A. Gentle·Michael Gutperle
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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.

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Simon A. Gentle, Michael Gutperle. 2014-07-21. Entanglement entropy of Wilson loops: Holography and matrix models. https://doi.org/10.1103/physrevd.90.066011

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