Mapping Cone Connections and their Yang-Mills 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_ | 1866912463475179520 |
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| author | Tseng, Li-Sheng Zhou, Jiawei |
| author_facet | Tseng, Li-Sheng Zhou, Jiawei |
| contents | For a given closed two-form, we introduce the cone Yang-Mills functional which is a Yang-Mills-type functional for a pair $(A,B)$, a connection one-form $A$ and a scalar $B$ taking value in the adjoint representation of a Lie group. The functional arises naturally from dimensionally reducing the Yang-Mills functional over the fiber of a circle bundle with the two-form being the Euler class. We write down the Euler-Lagrange equations of the functional and present some of the properties of its critical solutions, especially in comparison with Yang-Mills solutions. We show that a special class of three-dimensional solutions satisfy a duality condition which generalizes the Bogomolny monopole equations. Moreover, we analyze the zero solutions of the cone Yang-Mills functional and give an algebraic classification characterizing principal bundles that carry such cone-flat solutions when the two-form is non-degenerate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_01508 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mapping Cone Connections and their Yang-Mills Functional Tseng, Li-Sheng Zhou, Jiawei Differential Geometry High Energy Physics - Theory Symplectic Geometry For a given closed two-form, we introduce the cone Yang-Mills functional which is a Yang-Mills-type functional for a pair $(A,B)$, a connection one-form $A$ and a scalar $B$ taking value in the adjoint representation of a Lie group. The functional arises naturally from dimensionally reducing the Yang-Mills functional over the fiber of a circle bundle with the two-form being the Euler class. We write down the Euler-Lagrange equations of the functional and present some of the properties of its critical solutions, especially in comparison with Yang-Mills solutions. We show that a special class of three-dimensional solutions satisfy a duality condition which generalizes the Bogomolny monopole equations. Moreover, we analyze the zero solutions of the cone Yang-Mills functional and give an algebraic classification characterizing principal bundles that carry such cone-flat solutions when the two-form is non-degenerate. |
| title | Mapping Cone Connections and their Yang-Mills Functional |
| topic | Differential Geometry High Energy Physics - Theory Symplectic Geometry |
| url | https://arxiv.org/abs/2407.01508 |