Spectral Geometry with Exceptional Symmetry and Charged Higgs Fields
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911024780673024 |
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| author | Farnsworth, Shane |
| author_facet | Farnsworth, Shane |
| contents | We lay the foundations for a general approach to nonassociative spectral geometry as an extension of Connes' noncommutative geometry by explaining how to construct finite-dimensional, discrete spectral geometries with exceptional symmetry, and gauge covariant Dirac operators. We showcase an explicit construction of a geometry corresponding to the internal space of a $G_2\times G_2$ gauge theory with charged scalar content and scalar representations restricted by novel conditions arising from the associative properties of the coordinate algebra. Our construction motivates a new definition of bimodules over nonassociative algebras and a novel form of bimodule over semi-simple octonion algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_21496 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spectral Geometry with Exceptional Symmetry and Charged Higgs Fields Farnsworth, Shane Mathematical Physics High Energy Physics - Theory We lay the foundations for a general approach to nonassociative spectral geometry as an extension of Connes' noncommutative geometry by explaining how to construct finite-dimensional, discrete spectral geometries with exceptional symmetry, and gauge covariant Dirac operators. We showcase an explicit construction of a geometry corresponding to the internal space of a $G_2\times G_2$ gauge theory with charged scalar content and scalar representations restricted by novel conditions arising from the associative properties of the coordinate algebra. Our construction motivates a new definition of bimodules over nonassociative algebras and a novel form of bimodule over semi-simple octonion algebras. |
| title | Spectral Geometry with Exceptional Symmetry and Charged Higgs Fields |
| topic | Mathematical Physics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2506.21496 |