Concerning axially symmetric monopole-type solutions

Abstract

We study axially symmetric static, finite-energy solutions to Yang-Mills-Higgs field equations. The Lagrangian consists of a triplet of Higgs fields and a triplet of gauge fields and has local SO(3) gauge invariance. The solutions can describe, in principle, field configurations with arbitrary monopole charge. Although we have not found analytic solutions to the coupled partial differential equations involving six unknown functions, we do find consistent solutions in the asymptotic region as well as in the region near the axis of symmetry. We investigate the cylindrically symmetric configuration which is a particular case of our axially symmetric formulation and demonstrate that a vortex-type solution exists. We thus have a non-Abelian version of the Nielsen-Olesen model. We discuss the relevance of this vortex-type solution to our axially symmetric system and present plausibility arguments concerning the emergence of a non-Abelian stringlike configuration.