{"paper":{"title":"Electric-magnetic duality in the quantum double models of topological orders with gapped boundaries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-lat","math-ph","math.MP"],"primary_cat":"cond-mat.str-el","authors_text":"Hongyu Wang, Yidun Wan, Yingcheng Li, Yuting Hu","submitted_at":"2019-10-29T17:58:15Z","abstract_excerpt":"We generalize the Electric-magnetic (EM) duality in the quantum double (QD) models to the case of topological orders with gapped boundaries. We also map the QD models with boundaries to the Levin-Wen (LW) models with boundaries. To this end, we Fourier transform and rewrite the extended QD model with a finite gauge group $G$ on a trivalent lattice with a boundary. Gapped boundary conditions of the model before the transformation are known to be characterized by the subgroups $K \\subseteq G$. We find that after the transformation, the boundary conditions are then characterized by the Frobenius "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.13441","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/1910.13441/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"}