A $U(N)$ Gauge Theory in Three Dimensions as an Ensemble of Surfaces

TL;DR

This paper demonstrates that a specific three-dimensional $U(N)$ gauge theory on a dodecahedral lattice can be interpreted as a model of oriented self-avoiding surfaces, with partial solvability in the large $N$ limit.

Contribution

It introduces a novel interpretation of a $U(N)$ gauge theory as a surface model and discusses its partial solvability using large $N$ reduction.

Findings

The gauge theory corresponds to a model of oriented self-avoiding surfaces.

Partial solvability is achieved in the planar limit.

The model is defined on a three-dimensional dodecahedral lattice.

Abstract

A particular $U(N)$ gauge theory defined on the three dimensional dodecahedral lattice is shown to correspond to a model of oriented self-avoiding surfaces. Using large $N$ reduction it is argued that the model is partially soluble in the planar limit.