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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| Format: | Article |
| Language: | English |
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SpringerOpen
2024-12-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP12(2024)041 |
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| _version_ | 1846112964772364288 |
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| author | Ben Gripaios Khoi Le Nguyen Nguyen |
| author_facet | Ben Gripaios Khoi Le Nguyen Nguyen |
| author_sort | Ben Gripaios |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-ff39a8a8db2549288ddd6c0f145772fc |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-ff39a8a8db2549288ddd6c0f145772fc2024-12-22T12:09:22ZengSpringerOpenJournal of High Energy Physics1029-84792024-12-0120241212110.1007/JHEP12(2024)041Varieties of four-dimensional gauge theoriesBen Gripaios0Khoi Le Nguyen Nguyen1Cavendish Laboratory, University of CambridgeDAMTP, University of CambridgeAbstract 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.https://doi.org/10.1007/JHEP12(2024)041Anomalies in Field and String TheoriesGauge Symmetry |
| spellingShingle | Ben Gripaios Khoi Le Nguyen Nguyen Varieties of four-dimensional gauge theories Journal of High Energy Physics Anomalies in Field and String Theories Gauge Symmetry |
| title | Varieties of four-dimensional gauge theories |
| title_full | Varieties of four-dimensional gauge theories |
| title_fullStr | Varieties of four-dimensional gauge theories |
| title_full_unstemmed | Varieties of four-dimensional gauge theories |
| title_short | Varieties of four-dimensional gauge theories |
| title_sort | varieties of four dimensional gauge theories |
| topic | Anomalies in Field and String Theories Gauge Symmetry |
| url | https://doi.org/10.1007/JHEP12(2024)041 |
| work_keys_str_mv | AT bengripaios varietiesoffourdimensionalgaugetheories AT khoilenguyennguyen varietiesoffourdimensionalgaugetheories |