International Journal of Mathematics ( IF 0.604 ) Pub Date : 2020-07-31 , DOI: 10.1142/s0129167x20500809 M. Bischoff
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 with central charge depends on the “gravitational anomaly” . In particular, the conjecture that holomorphic permutation orbifolds are non-anomalous and therefore a stronger conjecture of Müger about braided crossed -categories arising from permutation orbifolds of completely rational conformal nets are wrong. More generally, we show that cyclic permutations of order are non-anomalous if and only if or . We also show that all cyclic permutation gaugings of arise from conformal nets.