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

Understand

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.