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.
Lorenzo Ruggeri (Fri,) studied this question.