1. Cohomological field theories and generalized Seiberg-Witten equations
- Author
-
Jiang, Shuhan and Jost, Jürgen
- Subjects
Mathematical Physics ,High Energy Physics - Theory - Abstract
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., Comment: 31 pages, 2 figures
- Published
- 2024