A Gauge-Independent Mechanism for Confinement and Mass Gap: Part II -- G=SU(2) and D=3

TL;DR

This paper explores a gauge-independent mechanism for confinement and mass gap in 3D SU(2) gauge theory using a dual spin foam framework, providing explicit formulas and analyzing their behavior.

Contribution

It introduces a novel gauge-independent approach to confinement in 3D SU(2) gauge theory via dual spin foam models, with explicit interaction formulas and asymptotic analysis.

Findings

Identification of interaction factors and their asymptotics.

Elementary properties of the dual theory supporting confinement.

Analysis of behavior in different sectors of the theory.

Abstract

We apply to the case of gauge group G = SU(2) in three dimensions a recently proposed gauge-independent mechanism for confinement that is based on a particular form of the dual spin foam framework for lattice gauge theory. Explicit formulae for interaction factors and their asymptotics are introduced and their behavior in different sectors of the theory are identified and analyzed. We arrive at several elementary properties of the dual theory that represent one scenario by which confinement may be realized at weak coupling. We conclude with an outlook for further development of this approach.