Mass gap in the weak coupling limit of $(2+1)$ SU(2) lattice gauge theory

TL;DR

This paper develops a dual description of 2+1 SU(2) lattice gauge theory using Schwinger bosons, enabling explicit Hilbert space construction and analysis of the mass gap in the weak coupling limit.

Contribution

It introduces a novel dual formulation with point splitting and Schwinger bosons, providing clearer insights into the gauge theory's dynamics and mass gap.

Findings

Explicit Hilbert space construction for gauge-invariant states

Analysis of loop dynamics in the weak coupling limit

Derivation of the mass gap in the model

Abstract

We develop the dual description of $2+1$ SU(2) lattice gauge theory as interacting `abelian like' electric loops by using Schwinger bosons. "Point splitting" of the lattice enables us to construct explicit Hilbert space for the gauge invariant theory which in turn makes dynamics more transparent. Using path integral representation in phase space, the interacting closed loop dynamics is analyzed in the weak coupling limit to get the mass gap.