Rigorous solution of strongly coupled $SO(N)$ lattice gauge theory in the large $N$ limit

Abstract

The main result of this paper is a rigorous computation of Wilson loop expectations in strongly coupled $SO(N)$ lattice gauge theory in the large $N$ limit, in any dimension. The formula appears as an absolutely convergent sum over trajectories in a kind of string theory on the lattice, demonstrating an explicit gauge-string duality. The generality of the proof technique may allow it to be extended other gauge groups.

61 pages. Minor revisions. To appear in Comm. Math. Phys