Moduli Space of Non-Abelian Vortices

Abstract

We completely determine the moduli space ${\mathcal{M}}_{N,k}$ of $k$ vortices in $U(N)$ gauge theory with $N$ Higgs fields in the fundamental representation. Its open subset for separated vortices is found as the symmetric product $(\mathbf{C}\ifmmode\times\else\texttimes\fi{}\mathbf{C}{P}^{N\ensuremath{-}1}{)}^{k}/{\mathfrak{S}}_{k}$. Orbifold singularities of this space correspond to coincident vortices and are resolved resulting in a smooth moduli manifold. The relation to K\"ahler quotient construction is discussed.