Heriot-Watt Mathematics Report Series
HWM07-13, 24 May 2007
Quiver gauge theory and noncommutative vortices
O Lechtenfeld, A D Popov and R J Szabo
Abstract
We construct explicit BPS and non-BPS solutions of the Yang-Mills equations on noncommutative spaces R_\theta^{2n} 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-invariant connection over R_\theta^{2n} 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_\theta^{2n}. 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 D0-branes inside a space-filling brane-antibrane system.
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