Moduli Space of Non-Abelian Vortices

TL;DR

This paper fully characterizes the moduli space of non-Abelian vortices in U(N) gauge theory, revealing its geometric structure, singularities, and resolutions, thereby advancing understanding of vortex configurations in gauge theories.

Contribution

It provides a complete description of the moduli space of k-vortices in U(N) gauge theory, including its geometric structure and singularity resolution.

Findings

The moduli space is the symmetric product (C x CP^{N-1})^k / S_k for separated vortices.

Orbifold singularities correspond to coincident vortices and are resolved into a smooth manifold.

The relation to Kahler quotient construction is established.

Abstract

We completely determine the moduli space 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 (C x CP^{N-1})^k / S_k. Orbifold singularities of this space correspond to coincident vortices and are resolved resulting in a smooth moduli manifold. Relation to Kahler quotient construction is discussed.