Heriot-Watt Mathematics Report Series
HWM05-3, 24 Mar 2005
Quiver Gauge Theory of Nonabelian Vortices and Noncommutative Instantons in Higher Dimensions
A D Popov and R J Szabo
Abstract
We construct explicit BPS and non-BPS solutions of the Yang-Mills
equations on the noncommutative space $R^{2n}_\theta\times S^2$ which have manifest rotational symmetry . Using SU(2)-equivariant dimensional reduction techniques, we show that the solutions imply an equivalence between instantons on $R^{2n}_\theta\times S^2$ and nonabelian vortices on $R^{2n}_\theta$, which can be interpreted as a blowing-up of a chain of D0-branes on $R^{2n}_\theta$ into a chain of spherical D2-branes on $R^{2n}_\theta\times S^2$. The low-energy dynamics of these
configurations is described by a quiver gauge theory which can be
formulated in terms of new geometrical objects generalizing
superconnections. This formalism enables the explicit assignment of
D0-brane charges in equivariant K-theory to the instanton solutions.
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