{"paper":{"title":"2-Group Symmetries of 3-dimensional Defect TQFTs and Their Gauging","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"Gauging the 0-form G-symmetry on the neutral component of a G-crossed braided fusion category produces its equivariantisation, which has a generalised symmetry that gauges back to the original.","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"math.QA","authors_text":"Benjamin Haake, Nils Carqueville","submitted_at":"2025-06-09T19:42:49Z","abstract_excerpt":"A large class of symmetries of topological quantum field theories is naturally described by functors into higher categories of topological defects. Here we study 2-group symmetries of 3-dimensional TQFTs. We explain that these symmetries can be gauged to produce new TQFTs iff certain defects satisfy the axioms of orbifold data. In the special case of Reshetikhin-Turaev theories coming from $G$-crossed braided fusion categories $\\mathcal C^\\times_G$, we show that there are 0- and 1-form symmetries which have no obstructions to gauging. We prove that gauging the 0-form $G$-symmetry on the neutra"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"In the special case of Reshetikhin-Turaev theories coming from G-crossed braided fusion categories C^×_G, we show that there are 0- and 1-form symmetries which have no obstructions to gauging. We prove that gauging the 0-form G-symmetry on the neutral component C_e of C^×_G produces its equivariantisation (C^×_G)^G, which in turn features a generalised symmetry whose gauging recovers C_e.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"These symmetries can be gauged to produce new TQFTs iff certain defects satisfy the axioms of orbifold data.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The paper proves that 2-group symmetries in 3D defect TQFTs from G-crossed braided fusion categories have no gauging obstructions and that gauging the 0-form G-symmetry on the neutral component produces the equivariantisation, with a reciprocal relation when G is commutative.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Gauging the 0-form G-symmetry on the neutral component of a G-crossed braided fusion category produces its equivariantisation, which has a generalised symmetry that gauges back to the original.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"6049eb5644905bd27979f77c92c99dd397e282c6c9cceb1d8268ede697fe32b8"},"source":{"id":"2506.08178","kind":"arxiv","version":1},"verdict":{"id":"0b7bff58-c00c-4910-9bd5-ae56ca48fc30","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T10:02:05.491511Z","strongest_claim":"In the special case of Reshetikhin-Turaev theories coming from G-crossed braided fusion categories C^×_G, we show that there are 0- and 1-form symmetries which have no obstructions to gauging. We prove that gauging the 0-form G-symmetry on the neutral component C_e of C^×_G produces its equivariantisation (C^×_G)^G, which in turn features a generalised symmetry whose gauging recovers C_e.","one_line_summary":"The paper proves that 2-group symmetries in 3D defect TQFTs from G-crossed braided fusion categories have no gauging obstructions and that gauging the 0-form G-symmetry on the neutral component produces the equivariantisation, with a reciprocal relation when G is commutative.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"These symmetries can be gauged to produce new TQFTs iff certain defects satisfy the axioms of orbifold data.","pith_extraction_headline":"Gauging the 0-form G-symmetry on the neutral component of a G-crossed braided fusion category produces its equivariantisation, which has a generalised symmetry that gauges back to the original."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.08178/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":14,"sample":[{"doi":"10.1016/j.aim","year":2009,"title":"Butterflies I: morphisms of 2-group stacks","work_id":"205a4c0b-4f21-473e-9076-6a75d74dc708","ref_index":1,"cited_arxiv_id":"0808.3627","is_internal_anchor":true},{"doi":"10.4064/bc114-2","year":2024,"title":"Lecture notes on two-dimensional defect TQFT , volume=","work_id":"28e67c1a-676d-4486-aaa4-64677c175af8","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2023,"title":"Orbifold completion of 3-categories","work_id":"35c911d0-0bae-474b-a2e5-571ed59368ba","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1007/s00220-","year":2016,"title":"The 1{Nexpansion of the symmetric traceless and the antisymmetric tensor models in rank three","work_id":"84bd055a-98f0-4018-b7c6-f88748b9a960","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2019,"title":"Orbifolds of n-dimensional defect TQFTs","work_id":"e1b0d4ab-1858-4778-9ef3-7e95b3555b47","ref_index":5,"cited_arxiv_id":"1705.06085","is_internal_anchor":true}],"resolved_work":14,"snapshot_sha256":"f4c2c2b389322b9ba9034f5cdeea856752ae3f19aab0b67c0303085bd23ea7df","internal_anchors":4},"formal_canon":{"evidence_count":2,"snapshot_sha256":"492fa9f9fdfd1817b80cc984f9532050a832925f58354c2c885e8ca891809d1a"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}