{"work":{"id":"28e2a1bd-ee47-4a88-87f3-7e54b1d5acdc","openalex_id":null,"doi":null,"arxiv_id":"1012.0911","raw_key":null,"title":"Surface operators in 3d Topological Field Theory and 2d Rational Conformal Field Theory","authors":null,"authors_text":"Kapustin, Anton and Saulina, Natalia","year":2010,"venue":"hep-th","abstract":"We study surface operators in 3d Topological Field Theory and their relations with 2d Rational Conformal Field Theory. We show that a surface operator gives rise to a consistent gluing of chiral and anti-chiral sectors in the 2d RCFT. The algebraic properties of the resulting 2d RCFT, such as the classification of symmetry-preserving boundary conditions, are expressed in terms of properties of the surface operator. We show that to every surface operator one may attach a Morita-equivalence class of symmetric Frobenius algebras in the ribbon category of bulk line operators. This provides a simple interpretation of the results of Fuchs, Runkel and Schweigert on the construction of 2d RCFTs from Frobenius algebras. We also show that every topological boundary condition in a 3d TFT gives rise to a commutative Frobenius algebra in the category of bulk line operators. We illustrate these general considerations by studying in detail surface operators in abelian Chern-Simons theory.","external_url":"https://arxiv.org/abs/1012.0911","cited_by_count":null,"metadata_source":"pith","metadata_fetched_at":"2026-05-24T09:58:22.766039+00:00","pith_arxiv_id":"1012.0911","created_at":"2026-05-11T11:41:05.936335+00:00","updated_at":"2026-05-24T09:58:22.766039+00:00","title_quality_ok":true,"display_title":"Surface operators in 3d Topological Field Theory and 2d Rational Conformal Field Theory","render_title":"Surface operators in 3d Topological Field Theory and 2d Rational Conformal Field Theory"},"hub":{"state":{"work_id":"28e2a1bd-ee47-4a88-87f3-7e54b1d5acdc","tier":"hub","tier_reason":"10+ Pith inbound or 1,000+ external citations","pith_inbound_count":10,"external_cited_by_count":null,"distinct_field_count":1,"first_pith_cited_at":"2021-11-01T18:00:00+00:00","last_pith_cited_at":"2026-05-19T14:47:50+00:00","author_build_status":"not_needed","summary_status":"needed","contexts_status":"needed","graph_status":"needed","ask_index_status":"not_needed","reader_status":"not_needed","recognition_status":"not_needed","updated_at":"2026-05-28T16:18:54.521395+00:00","tier_text":"hub"},"tier":"hub","role_counts":[{"context_role":"background","n":4}],"polarity_counts":[{"context_polarity":"background","n":4}],"runs":{},"summary":{},"graph":{},"authors":[]}}