New vortex ring configurations for the MAP dyon solutions

Abstract

Electrically charged magnetic solutions of SU(2) Yang-Mills-Higgs theory with net zero topological charge has been obtained as axially symmetric saddle-point solutions in Ref. [1]. These solutions are characterized by an integer, the winding number n of their azimuthal angle, φ, and an electric charge parameter, 0<η<1. In our work here we made further investigation into the properties of this MAP/vortex ring configuration with n=2, η=0.65 and varying Higgs field strength. Our observations showed that beside the fundamental solution which is an electrically charged MAP solution, there also exist two other branches of eclectically charged vortex ring solutions which both appear at λ=20.45. The difference in total energy between these two branches of solution is very small but the difference in diameter of vortex rings of the two branches is quite significant. Finding of a branching phenomena in presence of a fundamental MAP solution has been for the first time. In Ref. [2], new branching solutions occur for the electrically neutral case in presence of fundamental vortex ring solutions but not for the fundamental MAP solution.