Z(2) vortex solution in a field theory

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.