{"paper":{"title":"Almost flat highest weights and application to Wilson loops on compact surfaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MP","math.PR","math.RT"],"primary_cat":"math-ph","authors_text":"Thibaut Lemoine","submitted_at":"2023-03-20T17:22:00Z","abstract_excerpt":"We derive new formulas for the expectation and variance of Wilson loops for any contractible simple loop on a compact orientable surface of genus $1$ and higher, in the model of two-dimensional Yang--Mills theory with structure group $\\mathrm{U}(N)$. They are written in terms of a Gaussian measure on the dual of $\\mathrm{U}(N)$ introduced recently by the author and M. Ma\\\"ida \\cite{LM3}. From these formulas, we prove a quantitative result on the convergence of the expectation and variance as $N$ tends to infinity, refining a result of the author and A. Dahlqvist \\cite{DL}. We finally derive th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.11286","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2303.11286/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"}