A Candidate for Solvable Large N Lattice Gauge Theory in D>2

TL;DR

This paper introduces a class of large N lattice gauge theories in D≥2 that are dual to vector models, enabling analysis of their phase structure and Wilson loop averages through eigenvalue models and master-field representations.

Contribution

It proposes a new duality between lattice SU(N) gauge theories and vector models with specific symmetries, simplifying the study of large N limits and continuum behavior.

Findings

Partition function reduces to a one-matrix eigenvalue model at large N.

Derived a closed expression for Wilson loop averages on arbitrary 2D surfaces.

Identified a scaling condition for the continuum limit of the induced gauge theory.

Abstract

I propose a class of D\geq{2} lattice SU(N) gauge theories dual to certain vector models endowed with the local [U(N)]^{D} conjugation-invariance and Z_{N} gauge symmetry. In the latter models, both the partitition function and Wilson loop observables depend nontrivially only on the eigenvalues of the link-variables. Therefore, the vector-model facilitates a master-field representation of the large N loop-averages in the corresponding induced gauge system. As for the partitition function, in the limit N->{infinity} it is reduced to the 2Dth power of an effective one-matrix eigenvalue-model which makes the associated phase structure accessible. In particular a simple scaling-condition, that ensures the proper continuum limit of the induced gauge theory, is proposed. We also derive a closed expression for the large N average of a generic nonself-intersecting Wilson loop in the D=2 theory defined on an arbitrary 2d surface.