{"paper":{"title":"Varieties of four-dimensional gauge theories","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-ph","math.AG"],"primary_cat":"hep-th","authors_text":"Ben Gripaios, Khoi Le Nguyen Nguyen","submitted_at":"2024-09-23T18:00:11Z","abstract_excerpt":"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 algorith"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.15430","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2409.15430/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}