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

L. G. Aldrovandi·F. A. Schaposnik
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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.

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L. G. Aldrovandi, F. A. Schaposnik. 2007-02-27. Non-Abelian vortices in Chern-Simons theories and their induced effective theory. https://doi.org/10.1103/physrevd.76.045010

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