Monopoles in the Plaquette Formulation of the 3D SU(2) Lattice Gauge Theory

TL;DR

This paper investigates monopoles in 3D SU(2) lattice gauge theory using a plaquette formulation, deriving a dual sine-Gordon model to analyze monopole interactions and compute the string tension.

Contribution

It introduces a novel plaquette-based approach to monopoles, derives a dual sine-Gordon model for the Wilson loop, and calculates the string tension semiclassically.

Findings

Monopoles violate the continuum Bianchi identity in axial gauge.

A dual sine-Gordon model describes monopole interactions.

String tension is computed semiclassically.

Abstract

Using a plaquette formulation for lattice gauge models we describe monopoles of the three dimensional SU(2) theory which appear as configurations in the complete axial gauge and violate the continuum Bianchi identity. Furthemore we derive a dual formulation for the Wilson loop in arbitrary representation and calculate the form of the interaction between generated electric flux and monopoles in the region of a weak coupling relevant for the continuum limit. The effective theory which controls the interaction is of the sine-Gordon type model. The string tension is calculated within the semiclassical approximation.