{"paper":{"title":"Four flavours, triality and bimodular forms","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"hep-th","authors_text":"Elias Furrer, Jan Manschot, Johannes Aspman","submitted_at":"2021-10-22T18:00:01Z","abstract_excerpt":"We consider $\\mathcal{N}=2$ supersymmetric $\\text{SU}(2)$ gauge theory with $N_f=4$ massive hypermultiplets. The duality group of this theory contains transformations acting on the UV-coupling $\\tau_{\\text{UV}}$ as well as on the running coupling $\\tau$. We establish that subgroups of the duality group act separately on $\\tau_{\\text{UV}}$ and $\\tau$, while a larger group acts simultaneously on $\\tau_{\\text{UV}}$ and $\\tau$. For special choices of the masses, we find that the duality groups can be identified with congruence subgroups of $\\text{SL}(2,\\mathbb Z)$. We demonstrate that in such case"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.11969","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/2110.11969/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"}