{"paper":{"title":"A short proof of confinement in three-dimensional lattice gauge theories with a central $\\mathrm{U}(1)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-lat","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Sourav Chatterjee","submitted_at":"2026-01-31T01:16:53Z","abstract_excerpt":"Pure lattice gauge theories in three dimensions are widely expected to confine. A rigorous proof of confinement for three-dimensional $\\mathrm{U}(1)$ lattice gauge theory with Villain action was given by G\\\"opfert and Mack. Beyond the abelian case, rigorous confinement results are comparatively scarce; one general mechanism applies when the gauge group has a central copy of $\\mathrm{U}(1)$. Indeed, combining a comparison inequality of Fr{\\\"o}hlich with earlier work of Glimm and Jaffe yields confinement with a logarithmically growing quark-antiquark potential for this class of theories. The pur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.00436","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2602.00436/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"}