Explicit Construction of Hermitian Yang-Mills Instantons on Coset Manifolds
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916450217754624 |
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| author | Park, Jongmin Yang, Hyun Seok |
| author_facet | Park, Jongmin Yang, Hyun Seok |
| contents | In four dimensions, 't Hooft symbols offer a compact and powerful framework for describing the self-dual structures fundamental to instanton physics. Extending this to six dimensions, the six-dimensional 't Hooft symbols can be constructed using the isomorphism between the Lorentz group $Spin(6)$ and the unitary group $SU(4)$. We demonstrate that the six-dimensional self-dual structures governed by the Hermitian Yang-Mills equations can be elegantly organized using these generalized 't Hooft symbols. We also present a systematic method for constructing Hermitian Yang-Mills instantons from spin connections on six-dimensional manifolds using the generalized 't Hooft symbols. We provide a thorough analysis of the topological invariants such as instanton and Euler numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_09653 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Explicit Construction of Hermitian Yang-Mills Instantons on Coset Manifolds Park, Jongmin Yang, Hyun Seok High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics In four dimensions, 't Hooft symbols offer a compact and powerful framework for describing the self-dual structures fundamental to instanton physics. Extending this to six dimensions, the six-dimensional 't Hooft symbols can be constructed using the isomorphism between the Lorentz group $Spin(6)$ and the unitary group $SU(4)$. We demonstrate that the six-dimensional self-dual structures governed by the Hermitian Yang-Mills equations can be elegantly organized using these generalized 't Hooft symbols. We also present a systematic method for constructing Hermitian Yang-Mills instantons from spin connections on six-dimensional manifolds using the generalized 't Hooft symbols. We provide a thorough analysis of the topological invariants such as instanton and Euler numbers. |
| title | Explicit Construction of Hermitian Yang-Mills Instantons on Coset Manifolds |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics |
| url | https://arxiv.org/abs/2408.09653 |