Relating U(1) monopole configurations to SU(2) saddle-point configurations

Abstract

We have studied field configurations of the 3-dimensional Georgi-Glashow model which interpolate between the $U(1)$ and the $SU(2)$ limits. In the intermediate region, these configurations contain 't-Hooft--Polyakov monopoles. We use cooling and extremization to find these configurations and investigate their evolution as we adiabatically move towards the $U(1)$ and the $SU(2)$ limits. We also evolve an $SU(2)$ saddle point solution towards the $U(1)$ limit to see the relation between the unstable solutions in the $SU(2)$ theory and the stable ones in the $U(1)$ theory.