Topological twists of massive SQCD, Part I

TL;DR

This paper explores topological twists of 4D $ ext{SU}(2)$ $ ext{N}=2$ SQCD with up to 3 flavors, introducing background fluxes and arbitrary masses, and develops methods for evaluating the resulting path integrals on complex four-manifolds.

Contribution

It formulates twisted $ ext{N}=2$ SQCD theories with fluxes and masses on arbitrary four-manifolds, providing new techniques for low-energy path integral evaluation.

Findings

Formulation of theories with background fluxes on arbitrary bundles

Development of techniques for path integral evaluation with masses

Framework for explicit calculations in future work

Abstract

We consider topological twists of four-dimensional $\mathcal{N}=2$ supersymmetric QCD with gauge group SU(2) and $N_f\leq 3$ fundamental hypermultiplets. The twists are labelled by a choice of background fluxes for the flavour group, which provides an infinite family of topological partition functions. In this Part I, we demonstrate that in the presence of such fluxes the theories can be formulated for arbitrary gauge bundles on a compact four-manifold. Moreover, we consider arbitrary masses for the hypermultiplets, which introduce new intricacies for the evaluation of the low-energy path integral on the Coulomb branch. We develop techniques for the evaluation of these path integrals. In the forthcoming Part II, we will deal with the explicit evaluation.