{"paper":{"title":"Geometric Derivation of the Finite $N$ Master Loop Equation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-lat","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Omar Abdelghani, Ron Nissim","submitted_at":"2023-09-14T03:02:27Z","abstract_excerpt":"In this paper we provide a geometric derivation of the master loop equation for the lattice Yang-Mills model with structure group $G \\in \\{SO(N),SU(N), U(N)\\}$. This approach is based on integration by parts on $G$. In the appendix we compare our approach to that of \\cite{Ch19a} and \\cite{J16} based on Schwinger-Dyson equations, and \\cite{SheSmZh22} based on stochastic analysis. In particular these approaches are all easily seen to be equivalent. The novelty in our approach is the use of intrinsic geometry of $G$ which we believe simplifies the derivation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.07399","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2309.07399/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"}