Quiver Gauge Theory and Noncommutative Vortices
Abstract
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. 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.
Keywords
Cite
@article{arxiv.0706.0979,
title = {Quiver Gauge Theory and Noncommutative Vortices},
author = {Olaf Lechtenfeld and Alexander D. Popov and Richard J. Szabo},
journal= {arXiv preprint arXiv:0706.0979},
year = {2008}
}
Comments
talk by O.L. at the 21st Nishinomiya-Yukawa Memorial Symposium, Kyoto, 15 Nov. 2006