{"paper":{"title":"Renormalizability of the gradient flow in the 2D $O(N)$ non-linear sigma model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"hep-lat","authors_text":"Hiroki Makino, Hiroshi Suzuki","submitted_at":"2014-10-28T07:28:19Z","abstract_excerpt":"It is known that the gauge field and its composite operators evolved by the Yang--Mills gradient flow are ultraviolet (UV) finite without any multiplicative wave function renormalization. In this paper, we prove that the gradient flow in the 2D $O(N)$ non-linear sigma model possesses a similar property: The flowed $N$-vector field and its composite operators are UV finite without multiplicative wave function renormalization. Our proof in all orders of perturbation theory uses a $(2+1)$-dimensional field theoretical representation of the gradient flow, which possesses local gauge invariance wit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7538","kind":"arxiv","version":3},"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"}