Cohomological Localization of $\mathcal N = 2$ Gauge Theories with Matter

Understand

We construct a large class of gauge theories with extended supersymmetry on four-dimensional manifolds with a Killing vector field and isolated fixed points.

• We extend previous results limited to super Yang-Mills theory to general $\mathcal{N}=2$ gauge theories including hypermultiplets.
• We present a general framework encompassing equivariant Donaldson-Witten theory and Pestun's theory on $S^4$ as two particular cases.
• This is achieved by expressing fields in cohomological variables, whose features are dictated by supersymmetry and require a generalized notion of self-duality for two-forms and of chirality for spinors.