Group Theory of Non-Abelian Vortices

Abstract

We investigate the structure of the moduli space of multiple BPS non-Abelian vortices in U(N) gauge theory with N fundamental Higgs fields, focusing our attention on the action of the exact global (color-flavor diagonal) SU(N) symmetry on it. The moduli space of a single non-Abelian vortex, CP(N-1), is spanned by a vector in the fundamental representation of the global SU(N) symmetry. The moduli space of winding-number k vortices is instead spanned by vectors in the direct-product representation: they decompose into the sum of irreducible representations each of which is associated with a Young tableau made of k boxes, in a way somewhat similar to the standard group composition rule of SU(N) multiplets. The Kähler potential is exactly determined in each moduli subspace, corresponding to an irreducible SU(N) orbit of the highest-weight configuration.

LaTeX 46 pages, 4 figures

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• Non-Abelian Monopoles in the Higgs Phase
• Dynamics of Non-Abelian Vortices
• Vortex counting from field theory
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• Hilbert Series and Moduli Spaces of k U(N) Vortices
• Vortices on Orbifolds
• All Exact Solutions of Non-Abelian Vortices from Yang-Mills Instantons
• General Composite Non-Abelian Strings and Flag Manifold Sigma Models
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• The moduli space of non-Abelian vortices in Yang-Mills-Chern-Simons-Higgs theory