Noncommutative Multi-instantons on R ×s 2

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