Quiver gauge theory and noncommutative vortices

Abstract

We construct explicit BPS and non-BPS solutions of the Yang-Mills equations on noncommutative spaces ℝ2nθ × 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 ℝ2nθ × G/H. The U(k) Donaldson-Uhlenbeck-Yau equations on these spaces reduce to vortex-type equations in a particular quiver gauge theory on ℝ2nθ. Seiberg-Witten monopole equations are particular examples. The noncommutative BPS configurations are formulated with partial isometries, which are obtained from an equivariant Atiyah-Bott-Shapiro construction. They can be interpreted as DO-branes inside a space-filling brane-antibrane system.