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A remark about the anomalies of cyclic holomorphic permutation orbifolds
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 𝒜 with central charge c=8k depends on the “gravitational anomaly” k(mod3). In particular, the conjecture that holomorphic permutation orbifolds are non-anomalous and therefore a stronger conjecture of Müger about braided crossed Sn-categories arising from permutation orbifolds of completely rational conformal nets are wrong. More generally, we show that cyclic permutations of order n are non-anomalous if and only if 3n or 24|c. We also show that all cyclic permutation gaugings of Rep(𝒜) arise from conformal nets.

更新日期:2020-08-05

 

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