Wilson loop expectations in $SU(N)$ lattice gauge theory

Abstract: This article gives a rigorous formulation and proof of the $1/N$ expansion for Wilson loop expectations in strongly coupled $SU(N)$ lattice gauge theory in any dimension. The coefficients of the expansion are represented as absolutely convergent sums over trajectories in a string theory on the lattice, establishing a kind of gauge-string duality. Moreover, it is shown that in large $N$ limit, calculations in $SU(N)$ lattice gauge theory with coupling strength $2\beta$ corresponds to those in $SO(N)$ lattice gauge theory with coupling strength $\beta$ when $|\beta|$ is sufficiently small.