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

TL;DR

This paper rigorously computes Wilson loop expectations in strongly coupled $SO(N)$ lattice gauge theory at large $N$, revealing an explicit gauge-string duality through a convergent sum over lattice trajectories.

Contribution

It provides a rigorous derivation of Wilson loop expectations in $SO(N)$ gauge theory, establishing a gauge-string duality and a proof technique potentially applicable to other gauge groups.

Findings

Explicit formula as a convergent sum over lattice trajectories

Demonstration of gauge-string duality in the large $N$ limit

Potential extension of proof techniques to other gauge groups

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.