Quiver gauge theory of non-Abelian vortices and noncommutative instantons in higher dimensions

Alexander D. Popov, Richard J. Szabo

Research output: Contribution to journalArticle

49 Citations (Scopus)

Abstract

We construct explicit Bogomolnyi, Prasad, Sommerfeld (BPS) and non-BPS solutions of the Yang-Mills equations on the noncommutative space R? 2n × S2 which have manifest spherical symmetry. Using SU(2)-equivariant dimensional reduction techniques, we show that the solutions imply an equivalence between instantons on R? 2n × S2 and non-Abelian vortices on R? 2n, which can be interpreted as a blowing-up of a chain of D0 -branes on R? 2n into a chain of spherical D2 -branes on R? 2n × S2. 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. © 2006 American Institute of Physics.

Original languageEnglish
Pages (from-to)1-42
Number of pages42
JournalJournal of Mathematical Physics
Volume47
Issue number1
DOIs
Publication statusPublished - Jan 2006

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