Plaquette representation for 3D lattice gauge models: I. Formulation and perturbation theory

TL;DR

This paper introduces a plaquette-based analytical framework for 3D lattice gauge theories, simplifying non-abelian Bianchi identities and incorporating fermions, with a focus on perturbative expansions for U(1) and SU(N) models.

Contribution

It presents a modified plaquette formulation reducing connector complexity and extends it to include dynamical fermions, providing a foundation for non-abelian gauge theories.

Findings

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

Modified Batrouni formulation to simplify Bianchi identities.

Discussed the volume uniformity of the perturbative series.

Abstract

We develop an analytical approach for studying lattice gauge theories 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 only two connectors instead of four. In addition, we include dynamical fermions in the plaquette formulation. Using this representation we construct the low-temperature perturbative expansion for U(1) and SU(N) models and discuss its uniformity in the volume. The final aim of this study is to give a mathematical background for working with non-abelian models in the plaquette formulation.