Topological twists of massive SQCD, Part II

Abstract

This is the second and final part of ``Topological twists of massive SQCD''. Part I is available at arXiv:2206.08943. 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.

80 pages + appendices, 13 figures. Second part of a series of two papers, first part is available at arXiv:2206.08943. v2: published version