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

Abstract

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. Finally, we implement localization techniques to compute the exact partition function of the cohomological theories we built up and write the explicit result for manifolds with diverse topologies.

arXiv comment37 pages including appendices. Partial text overlap with arXiv:1812.06473 in appendices. Minor typo fixes, references added

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Cited by in corpus (6)

• Partition Functions and Fibering Operators on the Coulomb Branch of 5d SCFTs
• Conformal field theories on deformed spheres, anomalies, and supersymmetry
• Exact Results for SYM on $Y^{p,q}$ and $S^2\times S^2$ with Conical Singularities
• From 5d Flat Connections to 4d Fluxes (the Art of Slicing the Cone)
• Index of the Transversally Elliptic Complex in Pestunization
• Flavor deformations and supersymmetry enhancement in $4d$ $\mathcal{N}=2$ theories