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

Abstract

Non-Abelian vortices for a supersymmetric {\cal 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 {\cal N}=2 CP^{N-1} model. We analyze the quantum mechanics of this effective theory in the N=2 case.

arXiv commentCERN-PH-TH/2007-045

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• Fractional and semi-local non-Abelian Chern-Simons vortices
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• String Dynamics, Spontaneous Breaking of Supersymmetry and Dual Scalar Field Theory
• Local and Semi-local Vortices in Yang-Mills-Chern-Simons model
• The moduli space of non-Abelian vortices in Yang-Mills-Chern-Simons-Higgs theory