Non-Abelian vortices in Chern-Simons theories and their induced effective theory

Abstract

Non-Abelian vortices for a supersymmetric N = 2 Chern-Simons-Higgs theory are explicitly constructed. We introduce N Higgs fields in the fundamental representation of the U ( N) gauge group in order to have a color-flavor SU ( N) group remaining unbroken in the asymmetric phase. Bogomol’nyi-like first order equations are found and rotationally symmetric solutions are proposed. These solutions are shown to be truly non-Abelian by parameterizing them in terms of orientational collective coordinates. The low energy effective action for the orientational moduli results to be the one-dimensional supersymmetric N = 2 CP N − 1 model. We analyze the quantum mechanics of this effective theory in the N = 2 case.