MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( 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

Variational aspects of the generalized Seiberg-Witten functional

Wanjun Ai, Shuhan Jiang and Jürgen Jost


In this paper, as a step towards a unified mathematical treatment of the gauge functionals from quantum field theory that have found profound applications in mathematics, we generalize the Seiberg-Witten functional that in particular includes the Kapustin-Witten functional as a special case. We first demonstrate the smoothness of weak solutions to this generalized functional. We then establish the existence of weak solutions under the assumption that the structure group of the bundle is abelian, by verifying the Palais-Smale compactness.

MSC Codes:
seiberg-witten functional, Kapustin-Witten functional, Regularity of weak solutions, Palais--Smale compactness

Related publications

2024 Repository Open Access
Wanjun Ai, Shu-Han Jiang and Jürgen Jost

Variational aspects of the generalized Seiberg-Witten functional