Topological twists of massive SQCD, Part II

This is the second and final part of ‘Topological twists of massive SQCD’. Part I is available at Lett. Math. Phys. 114 (2024) 3, 62. In this second part, we evaluate the contribution of the Coulomb branch to topological path integrals for \(\mathcal {N}=2\) supersymmetric QCD with \(N_f\le 3\) massive hypermultiplets on compact four-manifolds. Our analysis includes the decoupling of hypermultiplets, the massless limit and the merging of mutually non-local singularities at the Argyres–Douglas points. We give explicit mass expansions for the four-manifolds \(\mathbb {P}^2\) and K3. For \(\mathbb {P}^2\), we find that the correlation functions are polynomial as function of the masses, while infinite series and (potential) singularities occur for K3. The mass dependence corresponds mathematically to the integration of the equivariant Chern class of the matter bundle over the moduli space of Q-fixed equations. We demonstrate that the physical partition functions agree with mathematical results on Segre numbers of instanton moduli spaces.