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Title: A remark about the anomalies of cyclic holomorphic permutation orbifolds
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 [Formula: see text] with central charge [Formula: see text] depends on the “gravitational anomaly” [Formula: see text]. In particular, the conjecture that holomorphic permutation orbifolds are non-anomalous and therefore a stronger conjecture of Müger about braided crossed [Formula: see text]-categories arising from permutation orbifolds of completely rational conformal nets are wrong. More generally, we show that cyclic permutations of order [Formula: see text] are non-anomalous if and only if [Formula: see text] or [Formula: see text]. We also show that all cyclic permutation gaugings of [Formula: see text] arise from conformal nets.  more » « less
Award ID(s):
1821162
PAR ID:
10311941
Author(s) / Creator(s):
Date Published:
Journal Name:
International Journal of Mathematics
Volume:
31
Issue:
10
ISSN:
0129-167X
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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