{"paper":{"title":"Topological Sectors and a Dichotomy in Conformal Field Theory","license":"","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"math.OA","authors_text":"Feng Xu, Roberto Longo","submitted_at":"2003-09-22T22:04:02Z","abstract_excerpt":"Let A be a local conformal net of factors on the circle with the split property. We provide a topological construction of soliton representations of the tensor product of n copies of A, that restrict to true representations of subnet inviant under cyclic permutations (cyclic orbifold). We prove a quantum index theorem for our sectors relating the Jones index to a topological degree. Then A is not completely rational iff the the cyclic orbifold has an irreducible representation with infinite index. This implies the following dichotomy: if all irreducible sectors of A have a conjugate sector the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0309366","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}