SU(3)-Equivariant Quiver Gauge Theories and Nonabelian Vortices

TL;DR

This paper explores SU(3)-equivariant dimensional reduction of Yang-Mills theory on specific Kaehler manifolds, deriving nonabelian vortex equations, constructing explicit solutions including noncommutative cases, and interpreting these as D-brane states.

Contribution

It provides a detailed analysis of SU(3)-equivariant reductions leading to nonabelian vortex equations and explicit solutions, extending methods to general compact Lie groups.

Findings

Explicit nonabelian vortex solutions on noncommutative spaces

Topological charge computations for these solutions

Interpretation of solutions as D-brane states

Abstract

We consider SU(3)-equivariant dimensional reduction of Yang-Mills theory on Kaehler manifolds of the form M x SU(3)/H, with H = SU(2) x U(1) or H = U(1) x U(1). The induced rank two quiver gauge theories on M are worked out in detail for representations of H which descend from a generic irreducible SU(3)-representation. The reduction of the Donaldson-Uhlenbeck-Yau equations on these spaces induces nonabelian quiver vortex equations on M, which we write down explicitly. When M is a noncommutative deformation of the space C^d, we construct explicit BPS and non-BPS solutions of finite energy for all cases. We compute their topological charges in three different ways and propose a novel interpretation of the configurations as states of D-branes. Our methods and results generalize from SU(3) to any compact Lie group.