Vortices and electrically charged vortices in non-Abelian gauge theories

Abstract

Vortex solutions for a spontaneously broken SU(N) theory are explicitly constructed. N Higgs fields in the adjoint representation are needed in order to ensure topological stability. (N-1) topologically different solutions exist with magnetic flux \ensuremath{\Phi} quantized according to the relation \ensuremath{\Phi}=(2\ensuremath{\pi}/e)n/ \ensuremath{\surd}N with n=1,2,...,N-1. When a Chern-Simons term is added, the model exhibits electrically charged vortex solutions. A novel feature of these solutions is that their electric charge q is quantized in units of the fundamental charge e, q=mne/ \ensuremath{\surd}2N , with m\ensuremath{\in}Z. In addition, their angular momentum J is nonzero and also quantized, J=nm/2N.