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

TL;DR

This paper constructs explicit non-Abelian vortex solutions in a supersymmetric Chern-Simons-Higgs theory, analyzes their properties, and derives the effective low-energy theory describing their orientational moduli, revealing a supersymmetric CP^{N-1} model.

Contribution

The paper explicitly constructs non-Abelian vortices in a supersymmetric Chern-Simons-Higgs theory and derives their effective low-energy dynamics as a supersymmetric CP^{N-1} model.

Findings

Explicit non-Abelian vortex solutions in supersymmetric Chern-Simons-Higgs theory.

Derivation of the effective action as a supersymmetric CP^{N-1} model.

Quantum analysis of the N=2 case of the 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.