Aspects of Electric and Magnetic Variables in SU(2) Yang-Mills Theory

TL;DR

This paper presents a new decomposition of SU(2) gauge fields revealing electric-magnetic symmetry and duality, suggesting a complex phase structure with confining strings and stable knotted solitons in Yang-Mills theory.

Contribution

It introduces a novel gauge field decomposition that emphasizes electric-magnetic symmetry and explores the resulting phase structure of SU(2) Yang-Mills theory.

Findings

Reveals a symmetry between electric and magnetic variables.

Proposes a phase involving a vector and scalar field with a mass scale.

Supports the existence of confining strings as knotted solitons.

Abstract

We introduce a novel decomposition of the four dimensional SU(2) gauge field. This decomposition realizes explicitely a symmetry between electric and magnetic variables, suggesting a duality picture between the corresponding phases. It also indicates that at large distances the Yang-Mills theory involves a three component unit vector field, a massive Lorentz vector field, and a neutral scalar field that condenses which yields the mass scale. Our results are consistent with the proposal that the physical spectrum of the theory contains confining strings which are tied into stable knotted solitons.