Rank Two Quiver Gauge Theory, Graded Connections and Noncommutative Vortices

Details Rank Two Quiver Gauge Theory, Graded Connections and Noncommutative Vortices Rank Two Quiver Gauge Theory, Graded Connections and Noncommutative Vortices

2006-03-29

arxiv.org/abs/hep-th/0603232v1

JHEP 0609:054,2006

Physics

High Energy Physics

High Energy Physics - Theory

1+39 pages

Scientific paper

10.1088/1126-6708/2006/09/054

We consider equivariant dimensional reduction of Yang-Mills theory on K"ahler manifolds of the form M times CP^1 times CP^1. This induces a rank two quiver gauge theory on M which can be formulated as a Yang-Mills theory of graded connections on M. The reduction of the Yang-Mills equations on M times CP^1 times CP^1 induces quiver gauge theory equations on M and quiver vortex equations in the BPS sector. When M is the noncommutative space R_theta^{2n} both BPS and non-BPS solutions are obtained, and interpreted as states of D-branes. Using the graded connection formalism, we assign D0-brane charges in equivariant K-theory to the quiver vortex configurations. Some categorical properties of these quiver brane configurations are also described in terms of the corresponding quiver representations.

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