The paper constructs BPS composite vortex strings whose worldsheet dynamics is a Flag manifold sigma model with couplings fixed by flux differences, and gives GLSM and NLSM formulations.
Group Theory of Non-Abelian Vortices
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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 K\"ahler potential is exactly determined in each moduli subspace, corresponding to an irreducible SU(N) orbit of the highest-weight configuration.
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General Composite Non-Abelian Strings and Flag Manifold Sigma Models
The paper constructs BPS composite vortex strings whose worldsheet dynamics is a Flag manifold sigma model with couplings fixed by flux differences, and gives GLSM and NLSM formulations.