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.

talk by O.L. at the 21st Nishinomiya-Yukawa Memorial Symposium, Kyoto, 15 Nov. 2006

Cited by in corpus (29)

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• Vortices as Instantons in Noncommutative Discrete Space: Use of $Z_2$ Coordinates
• Non Abelian Vortices as Instantons on Noncommutative Discrete Space
• Equivariant Fields in an $SU(\mathcal{N})$ Gauge Theory with new Spontaneously Generated Fuzzy Extra Dimensions
• Solitons and Yukawa Couplings in Nearly Kahler Flux Compactifications
• A $U(3)$ Gauge Theory on Fuzzy Extra Dimensions
• A ladder of topologically non-trivial non-BPS states