Noncommutative multi-instantons on R2n×S2

Generalizing self-duality on R2×S2 to higher dimensions, we consider the Donaldson–Uhlenbeck–Yau equations on R2n×S2 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 R2nθ. For a special S2-radius R depending on the noncommutativity θ we find explicit solutions in terms of shift operators. These vortex-like configurations on R2nθ determine SO(3)-invariant multi-instantons on R2nθ×S2R 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 S2 factor of suitable size.