2020/05/31 by Guido Festuccia, Anastasios Gorantis, Antonio Pittelli +2
Physics and Astronomy · #hep-th
paper · pdf · doi:10.1007/jhep09(2020)133
37 pages including appendices. Partial text overlap with arXiv:1812.06473 in appendices. Minor typo fixes, references added
arxiv created 2020/06/09 · arxiv updated 2020/10/28
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 N=2 gauge theories including hypermultiplets. We present a general framework encompassing equivariant Donaldson-Witten theory and Pestun's theory on S4 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.