Non-Abelian vortices of higher winding numbers

We make a detailed study of the moduli space of winding number two (k=2) axially symmetric vortices (or equivalently, of coaxial composite of two fundamental vortices), occurring in U(2) gauge theory with two flavors in the Higgs phase, recently discussed by Hashimoto and Tong and by Auzzi, Shifman, and Yung. We find that it is a weighted projective space WCP(2,1,1)2CP2/Z2. This manifold contains an A1-type (Z2) orbifold singularity even though the full moduli space including the relative position moduli is smooth. The SU(2) transformation properties of such vortices are studied. Our results are then generalized to U(N) gauge theory with N flavors, where the internal moduli space of k=2 axially symmetric vortices is found to be a weighted Grassmannian manifold. It contains singularities along a submanifold.