{"paper":{"title":"Dualities of $K$-theoretic Coulomb branches from a once-punctured torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.GT","math.QA"],"primary_cat":"math.RT","authors_text":"Dylan G. L. Allegretti, Peng Shan","submitted_at":"2024-11-26T12:39:12Z","abstract_excerpt":"We consider the quantized $\\mathrm{SL}_2$-character variety of a once-punctured torus. We show that this quantized algebra has three $\\mathbb{Z}_2$-invariant subalgebras that are isomorphic to quantized $K$-theoretic Coulomb branches in the sense of Braverman, Finkelberg, and Nakajima. These subalgebras are permuted by the $\\mathrm{SL}_2(\\mathbb{Z})$ mapping class group action. Our results confirm various predictions from the physics literature about 4d $\\mathcal{N}=2^*$ theories and their dualities."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.17378","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/2411.17378/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"}