Some noncommutative multi-instantons from vortices in curved space

We construct U(2) noncommutative multi-instanton solutions by extending Wittenʹs ansatz [1] which reduces the problem of cylindrical symmetry in four dimensions to that of a set of Bogomolʹnyi equations for an Abelian Higgs model in two-dimensional curved space. Using the Fock space approach, we give explicit vortex solutions to the Bogomolʹnyi equations and, from them, we present multi-instanton solutions.