Quiver Gauge Theory of Nonabelian Vortices and Noncommutative Instantons in Higher Dimensions

TL;DR

This paper constructs explicit solutions to Yang-Mills equations on noncommutative spaces, revealing a correspondence between instantons and nonabelian vortices, and introduces a quiver gauge theory framework with geometric generalizations.

Contribution

It demonstrates an equivalence between instantons and vortices on noncommutative spaces using equivariant reduction and introduces a new quiver gauge theory formalism with generalized superconnections.

Findings

Explicit BPS and non-BPS solutions on noncommutative space

Equivalence between instantons and vortices via dimensional reduction

A quiver gauge theory description with D-brane charge assignments

Abstract

We construct explicit BPS and non-BPS solutions of the Yang-Mills equations on the noncommutative space R^{2n}_\theta x S^2 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}_\theta x 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} x 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.