Noncommutative Multi-Instantons on R^{2n} x S^2

TL;DR

This paper constructs explicit noncommutative multi-instanton solutions on R^{2n} x S^2, extending self-duality concepts to higher dimensions and linking them to noncommutative D-brane configurations.

Contribution

It introduces a method to generate explicit noncommutative multi-instantons on R^{2n} x S^2 using SO(3) invariance and shift operators, generalizing self-duality to higher dimensions.

Findings

Explicit solutions for noncommutative multi-instantons on R^{2n} x S^2.

Reduction of equations to vortex-type equations via SO(3) invariance.

Interpretation of solutions as sub-branes in noncommutative D-brane systems.

Abstract

Generalizing self-duality on R^2 x S^2 to higher dimensions, we consider the Donaldson-Uhlenbeck-Yau equations on R^{2n} x S^2 and their noncommutative deformation for the gauge group U(2). Imposing SO(3) invariance (up to gauge transformations) reduces these equations to vortex-type equations for an abelian gauge field and a complex scalar on R^{2n}_\theta. For a special S^2-radius R depending on the noncommutativity \theta we find explicit solutions in terms of shift operators. These vortex-like configurations on R^{2n}_\theta determine SO(3)-invariant multi-instantons on R^{2n}_\theta x S^2_R for R=R(\theta). The latter may be interpreted as sub-branes of codimension 2n inside a coincident pair of noncommutative Dp-branes with an S^2 factor of suitable size.