Contour integral for the partition function of N = 2 topologically twisted on CP² and physical fluxes

A bstract We compute the contour integral for the partition function of an N N = 2 SU(2) topologically twisted theory on CP² CP 2 , dimensionally reducing from an N N = 1 theory on S 5 . Earlier works presented the partition function as a sum over three equivariant fluxes, one for each toric divisor of CP² CP 2 . Our result depends only on a single physical flux, assigned to the non-trivial two-cycle of the manifold. The reduced summation over fluxes is compensated by a contour of integration, arising from a different solution of the BPS equations, which captures more poles in each topological sector. As our observable involves a position-dependent Yang-Mills coupling, we compute new equivariant invariants of CP² CP 2 , which reduce to Donaldson invariants in the non-equivariant limit. Stability conditions of gauge bundles over CP² CP 2 appear intrinsically via the dimensional reduction.