Rank two quiver gauge theory, graded connections and noncommutative vortices

Olaf Lechtenfeld, Alexander D. Popov, Richard J. Szabo

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35 Citations (Scopus)


We consider equivariant dimensional reduction of Yang-Mills theory on Kähler manifolds of the form M × CP1 × CP1. 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 × CP1 × CP1 induces quiver gauge theory equations on M and quiver vortex equations in the BPS sector. When M is the noncommutative space R?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. © SISSA 2006.

Original languageEnglish
Article number054
JournalJournal of High Energy Physics
Issue number9
Publication statusPublished - 1 Sept 2006


  • Brane Dynamics in Gauge Theories
  • Non-Commutative Geometry
  • Solitons Monopoles and Instantons


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