Topological Classification of Symmetry Breaking and Vacuum Degeneracy
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911484054863872 |
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| author | Fischer, Simon-Raphael Farahani, Mehran Jalali Kim, Hyungrok Saemann, Christian |
| author_facet | Fischer, Simon-Raphael Farahani, Mehran Jalali Kim, Hyungrok Saemann, Christian |
| contents | We argue that a general system of scalar fields and gauge fields manifesting vacuum degeneracy induces a principal groupoid bundle over spacetime and that the pattern of spontaneous symmetry breaking and the Higgs mechanism are encoded by the singular foliation canonically induced on the moduli space of scalar vacuum expectation values by the Lie groupoid structure. Recent mathematical results in the classification of singular foliations then provide a qualitative classification of the possible patterns of vacuum degeneracy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_17634 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Topological Classification of Symmetry Breaking and Vacuum Degeneracy Fischer, Simon-Raphael Farahani, Mehran Jalali Kim, Hyungrok Saemann, Christian High Energy Physics - Theory Mathematical Physics Differential Geometry 53C12 (Primary) 70S15, 81T13, 57R30 (Secondary) We argue that a general system of scalar fields and gauge fields manifesting vacuum degeneracy induces a principal groupoid bundle over spacetime and that the pattern of spontaneous symmetry breaking and the Higgs mechanism are encoded by the singular foliation canonically induced on the moduli space of scalar vacuum expectation values by the Lie groupoid structure. Recent mathematical results in the classification of singular foliations then provide a qualitative classification of the possible patterns of vacuum degeneracy. |
| title | Topological Classification of Symmetry Breaking and Vacuum Degeneracy |
| topic | High Energy Physics - Theory Mathematical Physics Differential Geometry 53C12 (Primary) 70S15, 81T13, 57R30 (Secondary) |
| url | https://arxiv.org/abs/2406.17634 |