{"paper":{"title":"Two and four-loop $\\beta$-functions of rank 4 renormalizable tensor field theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Joseph Ben Geloun","submitted_at":"2012-05-24T17:49:21Z","abstract_excerpt":"A recent rank 4 tensor field model generating 4D simplicial manifolds has been proved to be renormalizable at all orders of perturbation theory [arXiv:1111.4997 [hep-th]]. The model is built out of $\\phi^6$ ($\\phi^6_{(1/2)}$), $\\phi^4$ ($\\phi^4_{(1)}$) interactions and an anomalous term ($\\phi^4_{(2)}$). The $\\beta$-functions of this model are evaluated at two and four loops. We find that the model is asymptotically free in the UV for both the main $\\phi^6_{(1/2)}$ interactions whereas it is safe in the $\\phi^4_{(1)}$ sector. The remaining anomalous term turns out to possess a Landau ghost."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5513","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":""},"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"}