{"paper":{"title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.str-el"],"primary_cat":"hep-th","authors_text":"Andreas Karch, Da-Chuan Lu, Ryan C. Spieler, Yasin F. Alam","submitted_at":"2026-07-22T18:00:03Z","abstract_excerpt":"The $\\mathrm{SL}(2,\\mathbb{Z})$ electromagnetic duality of 4d Maxwell theory induces theory-generating operations on 3d theories with $U(1)$ global symmetry. For theories with $U(1)^n$ symmetry, this structure generalizes to $\\mathrm{Sp}(2n,\\mathbb{Z})$. Focusing on the $U(1)^2$ case, we formulate the bulk $\\mathrm{Sp}(4,\\mathbb{Z})$ action and derive the corresponding boundary operations. We identify an intrinsically two-component element of order five, which generalizes the order-three $ST$ element of the single-$U(1)$ theory. Although its fifth power acts trivially in the bulk, the correspo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.20622","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/2607.20622/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"}