{"paper":{"title":"Asymptotic freedom in certain $SO(N)$ and $SU(N)$ models","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"hep-ph","authors_text":"D R Timothy Jones, Martin B Einhorn","submitted_at":"2017-05-02T00:59:31Z","abstract_excerpt":"We calculate the $\\beta$-functions for $SO(N)$ and $SU(N)$ gauge theories coupled to adjoint and fundamental scalar representations, correcting long-standing, previous results. We explore the constraints on $N$ resulting from requiring asymptotic freedom for all couplings. When we take into account the actual allowed behavior of the gauge coupling, the minimum value of $N$ in both cases turns out to be larger than realized in earlier treatments. We also show that in the large $N$ limit, both models have large regions of parameter space corresponding to total asymptotic freedom."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00751","kind":"arxiv","version":6},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}