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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.15430 |
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| _version_ | 1866908278812835840 |
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| author | Gripaios, Ben Nguyen, Khoi Le Nguyen |
| author_facet | Gripaios, Ben Nguyen, Khoi Le Nguyen |
| contents | We use algebraic geometry to study the anomaly-free representations of an arbitrary gauge Lie algebra for 4-dimensional spacetime fermions. For irreducible representations, the problem reduces to studying the Lie algebras $\mathfrak{su}_n$ for $n\geq 3$. We show that there exist equivalence classes of such representations that are in bijection with the rational points on a projective variety that are dense in a region of the underlying real variety diffeomorphic to $\mathbb{R}^{n-3}$. It follows that the chiral ones overwhelm the non-chiral ones for $n \geq 5$. We present an efficient algorithm to find explicit anomaly-free irreducible representations and discuss the generalization to reducible representations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_15430 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Varieties of four-dimensional gauge theories Gripaios, Ben Nguyen, Khoi Le Nguyen High Energy Physics - Theory High Energy Physics - Phenomenology Algebraic Geometry We use algebraic geometry to study the anomaly-free representations of an arbitrary gauge Lie algebra for 4-dimensional spacetime fermions. For irreducible representations, the problem reduces to studying the Lie algebras $\mathfrak{su}_n$ for $n\geq 3$. We show that there exist equivalence classes of such representations that are in bijection with the rational points on a projective variety that are dense in a region of the underlying real variety diffeomorphic to $\mathbb{R}^{n-3}$. It follows that the chiral ones overwhelm the non-chiral ones for $n \geq 5$. We present an efficient algorithm to find explicit anomaly-free irreducible representations and discuss the generalization to reducible representations. |
| title | Varieties of four-dimensional gauge theories |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology Algebraic Geometry |
| url | https://arxiv.org/abs/2409.15430 |