{"work":{"id":"07124b92-cd02-4853-b40a-93a21cd5a42d","openalex_id":null,"doi":null,"arxiv_id":"hep-th/0307041","raw_key":null,"title":"SL(2,Z) Action On Three-Dimensional Conformal Field Theories With Abelian Symmetry","authors":null,"authors_text":"Witten, Edward","year":2003,"venue":"hep-th","abstract":"On the space of three-dimensional conformal field theories with U(1) symmetry and a chosen coupling to a background gauge field, there is a natural action of the group $SL(2,{\\bf Z})$. The generator $S$ of $SL(2,{\\bf Z})$ acts by letting the background gauge field become dynamical, an operation considered recently by Kapustin and Strassler in explaining three-dimensional mirror symmetry. The other generator $T$ acts by shifting the Chern-Simons coupling of the background field. This $SL(2,{\\bf Z})$ action in three dimensions is related by the AdS/CFT correspondence to $SL(2,{\\bf Z})$ duality of low energy U(1) gauge fields in four dimensions.","external_url":"https://arxiv.org/abs/hep-th/0307041","cited_by_count":null,"metadata_source":"pith","metadata_fetched_at":"2026-07-04T16:09:56.876700+00:00","pith_arxiv_id":"hep-th/0307041","created_at":"2026-05-09T06:45:42.294591+00:00","updated_at":"2026-07-04T16:09:56.876700+00:00","title_quality_ok":true,"display_title":"SL(2,Z) Action On Three-Dimensional Conformal Field Theories With Abelian Symmetry","render_title":"SL(2,Z) Action On Three-Dimensional Conformal Field Theories With Abelian Symmetry"},"hub":{"state":{"work_id":"07124b92-cd02-4853-b40a-93a21cd5a42d","tier":"hub","tier_reason":"10+ Pith inbound or 1,000+ external citations","pith_inbound_count":14,"external_cited_by_count":null,"distinct_field_count":1,"first_pith_cited_at":"2025-06-11T07:08:51+00:00","last_pith_cited_at":"2026-06-29T18:00:03+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":"2026-08-05T02:34:30.776858+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":[]}}