{"paper":{"title":"Renormalization and Hopf Algebraic Structure of the 5-Dimensional Quartic Tensor Field Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.CO","math.MP"],"primary_cat":"math-ph","authors_text":"Adrian Tanasa, Remi Cocou Avohou, Vincent Rivasseau","submitted_at":"2015-07-13T18:50:09Z","abstract_excerpt":"This paper is devoted to the study of renormalization of the quartic melonic tensor model in dimension (=rank) five. We review the perturbative renormalization and the computation of the one loop beta function, confirming the asymptotic freedom of the model. We then define the Connes-Kreimer-like Hopf algebra describing the combinatorics of the renormalization of this model and we analyze in detail, at one- and two-loop levels, the Hochschild cohomology allowing to write the combinatorial Dyson-Schwinger equations. Feynman tensor graph Hopf subalgebras are also exhibited."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.03548","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":""},"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"}