Quiver Gauge Theory and Noncommutative Vortices

Understand

We construct explicit BPS and non-BPS solutions of the Yang-Mills equations on noncommutative spaces R^{2n}_theta x G/H which are manifestly G-symmetric.

• Given a G-representation, by twisting with a particular bundle over G/H, we obtain a G-equivariant U(k) bundle with a G-equivariant connection over R^{2n}_theta x G/H.
• The U(k) Donaldson-Uhlenbeck-Yau equations on these spaces reduce to vortex-type equations in a particular quiver gauge theory on R^{2n}_theta.
• Seiberg-Witten monopole equations are particular examples.