Reconstruction and local extensions for twisted group doubles, and permutation orbifolds
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- by David E. Evans and Terry Gannon PDF
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Abstract:
We prove the first nontrivial reconstruction theorem for modular tensor categories: the category associated to any twisted Drinfeld double of any finite group, can be realised as the representation category of a completely rational conformal net. We also show that any twisted double of a solvable group is the category of modules of a completely rational vertex operator algebra. In the process of doing this, we identify the 3-cocycle twist for permutation orbifolds of holomorphic conformal nets: unexpectedly, it can be nontrivial, and depends on the value of the central charge modulo 24. In addition, we determine the branching coefficients of all possible local (conformal) extensions of any finite group orbifold of holomorphic conformal nets, and identify their modular tensor categories.References
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Additional Information
- David E. Evans
- Affiliation: School of Mathematics, Cardiff University, Senghennydd Road, Cardiff CF24 4AG, Wales, United Kingdom
- MR Author ID: 64435
- Email: evansde@cf.ac.uk
- Terry Gannon
- Affiliation: Department of Mathematics, University of Alberta, Edmonton, Alberta T6G 2G1, Canada
- MR Author ID: 288922
- Email: tgannon@math.ualberta.ca
- Received by editor(s): October 9, 2020
- Received by editor(s) in revised form: October 4, 2021
- Published electronically: February 3, 2022
- Additional Notes: Their research was supported in part by EPSRC grant nos EP/K032208/1 and EP/N022432/1, PIMS, NSERC and SFB 878.
- © Copyright 2022 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 375 (2022), 2789-2826
- MSC (2020): Primary 46L80, 81T40; Secondary 81R05, 81R10, 81R15, 81T05
- DOI: https://doi.org/10.1090/tran/8575
- MathSciNet review: 4391734