{"paper":{"title":"Anomaly cancellation for a $U(1)$ factor","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":"2025-08-15T16:41:26Z","abstract_excerpt":"We use methods of arithmetic geometry to find solutions to the abelian local anomaly cancellation equations for a four-dimensional gauge theory whose Lie algebra has a single $\\mathfrak{u}_1$ summand, assuming that a non-trivial solution exists. The resulting polynomial equations in the integer $\\mathfrak{u}_1$ charges define a projective cubic hypersurface over the field of rational numbers. Generically, such a hypersurface is (by a theorem of Koll{\\'a}r) unirational, making it possible to find a finitely-many-to-one parameterization of infinitely many solutions using secant and tangent const"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.11583","kind":"arxiv","version":2},"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/2508.11583/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"}