Connected correlator of 1/2 BPS Wilson loops in $\mathcal{N}=4$ SYM

TL;DR

This paper derives exact finite N expressions for the connected correlator of 1/2 BPS Wilson loops in N=4 SYM and connects these results to topological recursion in matrix models.

Contribution

It provides the first exact finite N formula for the connected correlator of coincident 1/2 BPS Wilson loops and links it to Gaussian matrix model topological recursion.

Findings

Exact finite N expression for the connected correlator.

Reproduction of the 1/N expansion via topological recursion.

Exact generating function for Wilson loops in symmetric representation.

Abstract

We study the connected correlator of 1/2 BPS winding Wilson loops in $\mathcal{N}=4$ $U(N)$ super Yang-Mills theory, where those Wilson loops are on top of each other along the same circle. We find the exact finite $N$ expression of the connected correlator of such Wilson loops. We show that the $1/N$ expansion of this exact result is reproduced from the topological recursion of Gaussian matrix model. We also study the exact finite $N$ expression of the generating function of 1/2 BPS Wilson loops in the symmetric representation.