Phase transition of anti-symmetric Wilson loops in mathcal{N}=4 SYM

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 N2. 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.