{"paper":{"title":"Examples of Invertible Gauging via Orbifold Data, Zesting, and Equivariantisation","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"Zested orbifold data for symmetries related by zesting are Morita-equivalent and share the same surface defect.","cross_cats":["math-ph","math.MP","math.QA"],"primary_cat":"hep-th","authors_text":"Benjamin Haake","submitted_at":"2026-05-16T11:27:49Z","abstract_excerpt":"We study the gauging of invertible symmetries, particularly in 3 dimensions, using equivariantisation, $G$-crossed braided zesting, and the generalised orbifold construction. We discuss how these methods are related and illustrate them in various examples. We cover all $\\mathbb{Z}_2$-symmetries in Dijkgraaf--Witten $\\mathbb{Z}_2$-gauge theory $\\mathcal{D}(\\mathbb{Z}_2)$, the $\\mathbb{Z}_2$-symmetries described by Tambara--Yamagami categories, and obstructions to gauging the central symmetry in Chern--Simons $\\mathrm{SU}(2)_k$-gauge theory. We introduce zested orbifold data for symmetries relat"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We introduce zested orbifold data for symmetries related by zesting and show that the two associated orbifold data are Morita-equivalent, i.e. they have the same underlying surface defect.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The assumption that the generalised orbifold construction, equivariantisation, and G-crossed braided zesting can be applied consistently to the listed symmetries (Z2 in D(Z2), Tambara-Yamagami categories, and central symmetry in SU(2)_k Chern-Simons) without hidden obstructions beyond those already discussed.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Illustrates relations among gauging methods for invertible symmetries in 3D TQFTs and proves Morita equivalence of zested orbifold data for related symmetries.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Zested orbifold data for symmetries related by zesting are Morita-equivalent and share the same surface defect.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"bd8a12cb11e347fcc00c6bd55f486c619cfa1b63fe02cb0048efefe2df91870f"},"source":{"id":"2605.16942","kind":"arxiv","version":1},"verdict":{"id":"bde73b0e-bc11-4008-8a73-e47d5822c160","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T20:37:38.378781Z","strongest_claim":"We introduce zested orbifold data for symmetries related by zesting and show that the two associated orbifold data are Morita-equivalent, i.e. they have the same underlying surface defect.","one_line_summary":"Illustrates relations among gauging methods for invertible symmetries in 3D TQFTs and proves Morita equivalence of zested orbifold data for related symmetries.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The assumption that the generalised orbifold construction, equivariantisation, and G-crossed braided zesting can be applied consistently to the listed symmetries (Z2 in D(Z2), Tambara-Yamagami categories, and central symmetry in SU(2)_k Chern-Simons) without hidden obstructions beyond those already discussed.","pith_extraction_headline":"Zested orbifold data for symmetries related by zesting are Morita-equivalent and share the same surface defect."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.16942/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T21:01:19.120293Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T20:51:04.906001Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"cited_work_retraction","ran_at":"2026-05-19T20:21:57.220095Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T18:41:56.245351Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T18:33:26.327837Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"55fc821d19f55f38a1206139653cad11ae79c9fab1883def4c107d44dcd9f22c"},"references":{"count":96,"sample":[{"doi":"","year":null,"title":"Turaev, Vladimir , doi =","work_id":"a0a01eea-2bf8-4272-9554-4e81e0d968f8","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"On braided fusion categories I","work_id":"0007b013-c733-4953-a0a5-598fc51fa367","ref_index":2,"cited_arxiv_id":"0906.0620","is_internal_anchor":true},{"doi":"10.1155/s1073792803205079","year":2003,"title":"Module categories over the Drinfeld double of a finite group","work_id":"4888d9e1-a530-49c1-bd95-aae2acb1d489","ref_index":3,"cited_arxiv_id":"math/0202130","is_internal_anchor":true},{"doi":"","year":null,"title":"Tensor categories , url =","work_id":"000a2ebc-8362-4659-a6ed-f56afbc4cf34","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1016/j.jalgebra.2015.01.014","year":2015,"title":"The pivotal cover and Frobenius-Schur indicators","work_id":"7057d1a5-ea5c-491d-bbce-1e9b8f4e701d","ref_index":5,"cited_arxiv_id":"1309.4539","is_internal_anchor":true}],"resolved_work":96,"snapshot_sha256":"be812336feda55d24b81d82df408baf1765f059a2f376198d2256fdfb1cd5e70","internal_anchors":19},"formal_canon":{"evidence_count":2,"snapshot_sha256":"d721a7f105fa73bff287f8c35b8782afd9619b40b6451f4fe67ba1409d51c360"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}