Varieties of four-dimensional gauge theories
Abstract 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 𝔰𝔲 n for n ≥ 3. We show that there exist equivalence classes of such...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2024-12-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP12(2024)041 |
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| Summary: | Abstract 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 𝔰𝔲 n for n ≥ 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 on the underlying real variety diffeomorphic to ℝ n−3. It follows that the chiral ones overwhelm the non-chiral ones for n ≥ 5. We present an efficient algorithm to find explicit anomaly-free irreducible representations and discuss the generalization to reducible representations. |
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| ISSN: | 1029-8479 |