{"paper":{"title":"A remark about the anomalies of cyclic holomorphic permutation orbifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.QA"],"primary_cat":"math-ph","authors_text":"Marcel Bischoff","submitted_at":"2018-12-31T17:34:14Z","abstract_excerpt":"Using a result of Longo and Xu, we show that the anomaly arising from a cyclic permutation orbifold of order 3 of a holomorphic conformal net $\\mathcal A$ with central charge $c=8k$ depends on the \"gravitational anomaly\" $k\\pmod 3$. In particular, the conjecture that holomorphic permutation orbifolds are non-anomalous and therefore a stronger conjecture of M\\\"uger about braided crossed $S_n$-categories arising from permutation orbifolds of completely rational conformal nets are wrong. More general, we show that cyclic permutations of order $n$ are non-anomalous if and only if $3\\nmid n$ or $24"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.11910","kind":"arxiv","version":1},"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"}