Group Theory of Non-Abelian Vortices

Understand

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.