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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2508.19375 |
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| _version_ | 1866917140403060736 |
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| author | Schmidtt, David M. |
| author_facet | Schmidtt, David M. |
| contents | We refine and generalize the results of e-Print: 2307.10428 [hep-th], where evidence in favor of applying the non-Abelian localization method to handle the 4d Chern-Simons theory path integral formulation was presented. We show, via duality manipulations and invoking some symplectic geometry results, both inspired by the Beasley-Witten work e-Print: 0503126 [hep-th], that the path integral of a regularized version of the 4d Chern-Simons theory, formally takes the canonical symplectic form required by the method of non-Abelian localization. The new theory is defined on a deformed quotient space and interpolates between the conventional 3d Chern-Simons theory on a Seifert manifold M e-Print: 0503126 [hep-th], trivially embedded into $\mathbb{R}\times \text{M}$, and the Costello-Yamazaki e-Print: 1908.02289 [hep-th] 4d Chern-Simons theory defined on the same 4d manifold. It is also shown that the regularized theory is consistent, following an idea of Beasley e-Print: 0911.2687 [hep-th], with the insertion of coadjoint orbit defects of the 1d Chern-Simons theory type. This approach opens the possibility for using exact path integral methods to explore the quantum integrable structure of certain 2d integrable sigma models of the non-ultralocal type, which are widely known to be somehow immune to the use of more traditional quantization methods, like the algebraic Bethe ansatz. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_19375 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Contact 4d Chern-Simons theory: Generalities Schmidtt, David M. High Energy Physics - Theory We refine and generalize the results of e-Print: 2307.10428 [hep-th], where evidence in favor of applying the non-Abelian localization method to handle the 4d Chern-Simons theory path integral formulation was presented. We show, via duality manipulations and invoking some symplectic geometry results, both inspired by the Beasley-Witten work e-Print: 0503126 [hep-th], that the path integral of a regularized version of the 4d Chern-Simons theory, formally takes the canonical symplectic form required by the method of non-Abelian localization. The new theory is defined on a deformed quotient space and interpolates between the conventional 3d Chern-Simons theory on a Seifert manifold M e-Print: 0503126 [hep-th], trivially embedded into $\mathbb{R}\times \text{M}$, and the Costello-Yamazaki e-Print: 1908.02289 [hep-th] 4d Chern-Simons theory defined on the same 4d manifold. It is also shown that the regularized theory is consistent, following an idea of Beasley e-Print: 0911.2687 [hep-th], with the insertion of coadjoint orbit defects of the 1d Chern-Simons theory type. This approach opens the possibility for using exact path integral methods to explore the quantum integrable structure of certain 2d integrable sigma models of the non-ultralocal type, which are widely known to be somehow immune to the use of more traditional quantization methods, like the algebraic Bethe ansatz. |
| title | Contact 4d Chern-Simons theory: Generalities |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2508.19375 |