A center vortex representaton of the classical SU(2) vacuum

TL;DR

This paper presents a non-perturbative classical SU(2) vacuum model based on center vortices, which resembles the quantum vacuum and can be broken by perturbations, offering insights into gauge theory vacua.

Contribution

It introduces a classical center vortex representation of the SU(2) vacuum that parallels quantum vacuum structures and discusses how perturbations can break this trivial configuration.

Findings

Classical SU(2) vacuum can be represented as a lattice of center vortex pairs.

Perturbations such as mass terms or quantum fluctuations can break the trivial vortex lattice.

The vortex structure provides a bridge between classical and quantum descriptions of the vacuum.

Abstract

The classical massless SU(2) field theory has an infinite number of gauge equivalent representations of the vacuum. We show that among these there exists a non-perturbative center vortex representation with some similarity to the quantum vacuum of the same theory. This classical SU(2) vacuum consists of a lattice of center vortex pairs combining to triviality. However, this triviality can be broken by perturbations, for example by adding a mass term, or by considering the electroweak theory where the Higgs field does the breaking, or by quantum fluctuations like in QCD.