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

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.