Lattice Yang-Mills theories are important models in particle physics. They are defined on the d-dimensional lattice $\mathbb{Z}^d$ using a group of matrices of dimension N, and Wilson loop expectations are the fundamental observables of these theories. Recently, Cao, Park, and Sheffield showed that Wilson loop expectations can be expressed as sums over certain embedded bipartite maps of any genus. Building on this novel approach, we prove in the so-called strongly coupled regime:
- A rigorous formula in terms of embedded bipartite planar maps of Wilson loop expectations in the large N limit, in any dimension d.
- An exact computation of Wilson loop expectations in the large N limit, in dimension $d=2$.