Analytical study of low temperature phase of 3D LGT in the plaquette formulation

TL;DR

This paper develops an analytical framework for non-abelian gauge models in the plaquette formulation, enabling low-temperature expansions and dual representations, which enhance understanding of phase structures in 3D lattice gauge theories.

Contribution

It introduces a modified plaquette-based approach with simplified Bianchi identities and constructs low-temperature expansions and dual representations for non-abelian gauge models.

Findings

Constructed low-temperature expansion for U(1) and SU(N) models.

Derived dual representation for the 't Hooft loop in SU(2).

Discussed monopoles in the maximal axial gauge.

Abstract

We develop an analytical approach for non-abelian gauge models within the plaquette representation where the plaquette matrices play the role of the fundamental degrees of freedom. We start from the original Batrouni formulation and show how it can be modified in such a way that each non-abelian Bianchi identity contains two connectors instead of four. Using this representation we construct the low-temperature expansion for U(1) and SU(N) models on a finite lattice and discuss its uniformity in the volume. Next, we derive a dual representation for the 't Hooft loop in the SU(2) model and describe monopoles in the maximal axial gauge.