Wilson Loops in ${\cal N}=4$ Supersymmetric Yang-Mills Theory from Random Matrix Theory

TL;DR

This paper demonstrates that Wilson loops in ${ m extbf{N}=4}$ supersymmetric Yang-Mills theory can be derived from Random Matrix Theory, showing insensitivity to potential details and computing higher correlation functions for arbitrary representations.

Contribution

It establishes the universality of Wilson loop results from Random Matrix Theory and computes higher k-point functions for arbitrary U(N) representations.

Findings

Wilson loop results are insensitive to potential details

Higher k-point correlation functions are computed for arbitrary representations

Results align with AdS/CFT predictions

Abstract

Based on the AdS/CFT correspondence, string theory has given exact predictions for circular Wilson loops in U(N) ${\cal N}=4$ supersymmetric Yang-Mills theory to all orders in a 1/N expansion. These Wilson loops can also be derived from Random Matrix Theory. In this paper we show that the result is generically insensitive to details of the Random Matrix Theory potential. We also compute all higher $k$-point correlation functions, which are needed for the evaluation of Wilson loops in arbitrary irreducible representations of U(N).