Variational aspects of the generalized Seiberg-Witten functional
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913199493742592 |
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| author | Ai, Wanjun Jiang, Shuhan Jost, Jürgen |
| author_facet | Ai, Wanjun Jiang, Shuhan Jost, Jürgen |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_09924 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Variational aspects of the generalized Seiberg-Witten functional Ai, Wanjun Jiang, Shuhan Jost, Jürgen Analysis of PDEs 58E15 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. |
| title | Variational aspects of the generalized Seiberg-Witten functional |
| topic | Analysis of PDEs 58E15 |
| url | https://arxiv.org/abs/2401.09924 |