{"paper":{"title":"Topological Responses of the Standard Model Gauge Group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.str-el","hep-ph"],"primary_cat":"hep-th","authors_text":"Juven Wang, Yi-Zhuang You, Zheyan Wan","submitted_at":"2024-12-30T18:58:07Z","abstract_excerpt":"The local Lie algebra of the Standard Model (SM) is $su(3)\\times su(2) \\times u(1)$, yet its global gauge group, $G_{{\\rm SM}_{\\rm q}}=$SU(3)$\\times$SU(2)$\\times$U(1)/$\\mathbb{Z}_{\\rm q}$, q$=1,2,3,6$ remains undetermined. Building on previous work on 4d anomalies and 5d cobordism invariants, we classify lower-dimensional invertible field theories (iFTs) or symmetry-protected topological states (SPTs) in 4d, 3d, 2d, and 1d. While the integer SPTs are hard to detect, the fractional SPTs produce measurable topological responses. In particular, the symmetry fractionalization labeled by $k\\in\\math"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.21196","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/2412.21196/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"}