An Algebraic Roadmap of Particle Theories, Part III: Intersections
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866912232470740992 |
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| author | Furey, N. |
| author_facet | Furey, N. |
| contents | In this article, we bypass the detailed symmetry breaking pathways established in [1]. Instead, a direct route from the Spin(10) model to the Standard Model is enabled via a single algebraic constraint. This single constraint, however, may be reconfigured as a requirement that three $\mathfrak{so}(10)$ actions coincide on a fixed space of multi-vector fermions. This $\mathfrak{so}(10) \mapsto \mathfrak{su}(3)_{C} \oplus \mathfrak{su}(2)_{L} \oplus{u}(1)_{Y}$ breaking (from a three-way intersection) mirrors, in certain ways, the $\mathfrak{so}(8) \mapsto \mathfrak{g}_2$ breaking (from a three-way intersection) in the context of octonionic triality. By extending this result to include quaternions and complex numbers, we find that a five-way intersection breaks $\mathfrak{so}(10) \mapsto \mathfrak{su}(3)_{C} \oplus \mathfrak{u}(1)_{Q}$. These are the Standard Model's unbroken gauge symmetries, post-Higgs-mechanism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_14207 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An Algebraic Roadmap of Particle Theories, Part III: Intersections Furey, N. High Energy Physics - Phenomenology High Energy Physics - Theory In this article, we bypass the detailed symmetry breaking pathways established in [1]. Instead, a direct route from the Spin(10) model to the Standard Model is enabled via a single algebraic constraint. This single constraint, however, may be reconfigured as a requirement that three $\mathfrak{so}(10)$ actions coincide on a fixed space of multi-vector fermions. This $\mathfrak{so}(10) \mapsto \mathfrak{su}(3)_{C} \oplus \mathfrak{su}(2)_{L} \oplus{u}(1)_{Y}$ breaking (from a three-way intersection) mirrors, in certain ways, the $\mathfrak{so}(8) \mapsto \mathfrak{g}_2$ breaking (from a three-way intersection) in the context of octonionic triality. By extending this result to include quaternions and complex numbers, we find that a five-way intersection breaks $\mathfrak{so}(10) \mapsto \mathfrak{su}(3)_{C} \oplus \mathfrak{u}(1)_{Q}$. These are the Standard Model's unbroken gauge symmetries, post-Higgs-mechanism. |
| title | An Algebraic Roadmap of Particle Theories, Part III: Intersections |
| topic | High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2312.14207 |