Moduli spaces of instantons on toric noncommutative manifolds

We study analytic aspects of U(n) gauge theory over a toric noncommutative manifold. We analyse moduli spaces of solutions to the self- dual Yang–Mills equations on U(2) vector bundles over four-manifolds, showing that each such moduli space is either empty or a smooth Hausdorff manifold whose dimension we explicitly compute. In the spe- cial case of the four-sphere Sθ4 we find that the moduli space of U(2) instantons with fixed second Chern number k is a smooth manifold of dimension 8k − 3.