Phase Transition of Anti-Symmetric Wilson Loops in $\mathcal{N}=4$ SYM

TL;DR

This paper investigates a phase transition in 1/2 BPS Wilson loops within anti-symmetric representations of $ 4$ SYM, revealing a transition between one-cut and two-cut phases at a critical 't Hooft coupling, with implications for matrix model computations.

Contribution

It demonstrates the existence of a phase transition in Wilson loops in anti-symmetric representations and connects this to matrix model phase structures and topological recursion methods.

Findings

Identifies a phase transition at a critical 't Hooft coupling of order N^2.

Shows the one-cut phase is connected to small coupling regimes.

Provides a systematic way to compute $1/N$ corrections using topological recursion.

Abstract

We will argue that the 1/2 BPS Wilson loops in the anti-symmetric representations in the $\mathcal{N}=4$ super Yang-Mills (SYM) theory exhibit a phase transition at some critical value of the 't Hooft coupling of order $N^2$. In the matrix model computation of Wilson loop expectation values, this phase transition corresponds to the transition between the one-cut phase and the two-cut phase. It turns out that the one-cut phase is smoothly connected to the small 't Hooft coupling regime and the $1/N$ corrections of Wilson loops in this phase can be systematically computed from the topological recursion in the Gaussian matrix model.