{"paper":{"title":"Two $\\beta$-ensemble realization of $\\beta$-deformed WLZZ models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"A. Mironov, A. Oreshina, A. Popolitov","submitted_at":"2024-03-09T17:11:50Z","abstract_excerpt":"We consider a two $\\beta$-ensemble realization of the series of $\\beta$-deformed WLZZ matrix models. We demonstrate that such a realization involves $\\beta$-deformed Harish-Chandra-Itzykson-Zuber integrals, one of them providing a coupling to the external field. We also construct Ward identities in the corresponding two $\\beta$-ensemble model, which requires a set of identities for partition function of the one $\\beta$-ensemble in the external field, and a set of identities for the $\\beta$-deformed Itzykson-Zuber integral. These both sets of identities are formulated in terms of the Dunkl oper"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.05965","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/2403.05965/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"}