Rank two quiver gauge theory, graded connections and noncommutative vortices

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

doi:10.1088/1126-6708/2006/09/054

Rank two quiver gauge theory, graded connections and noncommutative vortices

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

Research output: Contribution to journal › Article › peer-review

32 Citations (Scopus)

Abstract

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 language	English
Article number	054
Journal	Journal of High Energy Physics
Volume	2006
Issue number	9
DOIs	https://doi.org/10.1088/1126-6708/2006/09/054
Publication status	Published - 1 Sep 2006

Keywords

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

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10.1088/1126-6708/2006/09/054

Cite this

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title = "Rank two quiver gauge theory, graded connections and noncommutative vortices",

abstract = "We consider equivariant dimensional reduction of Yang-Mills theory on K{\"a}hler 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. {\textcopyright} SISSA 2006.",

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AU - Lechtenfeld, Olaf

AU - Popov, Alexander D.

AU - Szabo, Richard J.

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AB - 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.

KW - Brane Dynamics in Gauge Theories

KW - Non-Commutative Geometry

KW - Solitons Monopoles and Instantons

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DO - 10.1088/1126-6708/2006/09/054

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JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

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ER -

Rank two quiver gauge theory, graded connections and noncommutative vortices

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