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

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}_θ. For a special S^2-radius R depending on the noncommutativity θwe find explicit solutions in terms of shift operators. These vortex-like configurations on R^{2n}_θdetermine SO(3)-invariant multi-instantons on R^{2n}_θx S^2_R for R=R(θ). 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.