Z(2) vortex solution in a field theory

TL;DR

This paper introduces a finite energy Z(2) vortex solution in a 2+1D SO(3) gauge theory with a Higgs field, revealing its topological properties and effects on Wilson loops, with implications for confinement.

Contribution

It presents a novel Z(2) vortex solution with unique topological and physical properties in a gauge theory context.

Findings

Vortex carries Z(2) magnetic charge and obeys modulo two addition.

Vortex core resembles Abrikosov vortex in superconductors.

Dilute gas of vortices induces area law behavior in Wilson loops.

Abstract

We present a finite energy topological Z(2) vortex solution in a 2+1 dimensional SO(3) gauge field theory minimally coupled to a matrix valued Higgs field. The vortex carries a Z(2) magnetic charge and obeys a modulo two addition property. The core of this vortex has a structure similar to that of the Abrikosov vortex appearing in a type II superconductor. The implications of this solution for Wilson loops are quite interesting. In two Euclidean dimensions these vortices are instantons and a dilute gas of such vortices disorders Wilson loops producing an area law behaviour with an exponentially small string tension. In 2+1 dimensions the vortices are loops and they affect the same disordering in the phase having large loops.