We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
MiS Preprint
48/2024
Cohomological field theories and generalized Seiberg-Witten equations
We introduce a formalism for constructing cohomological field theories (CohFT) out of nonlinear PDEs based on the first author's previous work (arXiv:2202.12425). We apply the formalism to the generalized Seiberg-Witten equations and show that the obtained CohFT functionals agree with the existing ones proposed by physicists. This leads to a unified perspective from which to view the full supersymmetric functionals of the Donaldson-Witten, Seiberg-Witten, and Kapustin-Witten theories and understand the relations between them. We also outline a quantization program for our framework and discuss its potential to produce manifold invariants and quantum cohomologies.
