The $1/N$ expansion for $SO(N)$ lattice gauge theory at strong coupling

Sourav Chatterjee, Jafar Jafarov

Published 2016-04-16Version 1

The $1/N$ expansion is an asymptotic series expansion for certain quantities in large-$N$ lattice gauge theories. This article gives a rigorous formulation and proof of the $1/N$ expansion for Wilson loop expectations in $SO(N)$ lattice gauge theory in the strong coupling regime in any dimension. The terms in the expansion are expressed as sums over trajectories of strings in a lattice string theory, establishing an explicit gauge-string duality. The trajectories trace out surfaces of genus zero for the first term in the expansion, and surfaces of higher genus for the higher terms.