Modularity of logarithmic parafermion vertex algebras
Auger J, Creutzig T, Ridout D (2018)
Publication Type: Journal article
Publication year: 2018
Journal
Book Volume: 108
Pages Range: 2543-2587
Journal Issue: 12
DOI: 10.1007/s11005-018-1098-4
Abstract
The parafermionic cosets Ck= Com (H, Lk(sl2)) are studied for negative admissible levels k, as are certain infinite-order simple current extensions Bk of Ck. Under the assumption that the tensor theory considerations of Huang, Lepowsky and Zhang apply to Ck, irreducible Ck- and Bk-modules are obtained from those of Lk(sl2). Assuming the validity of a certain Verlinde-type formula likewise gives the Grothendieck fusion rules of these irreducible modules. Notably, there are only finitely many irreducible Bk-modules. The irreducible Ck- and Bk-characters are computed and the latter are shown, when supplemented by pseudotraces, to carry a finite-dimensional representation of the modular group. The natural conjecture then is that the Bk are C2-cofinite vertex operator algebras.
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How to cite
APA:
Auger, J., Creutzig, T., & Ridout, D. (2018). Modularity of logarithmic parafermion vertex algebras. Letters in Mathematical Physics, 108(12), 2543-2587. https://doi.org/10.1007/s11005-018-1098-4
MLA:
Auger, Jean, Thomas Creutzig, and David Ridout. "Modularity of logarithmic parafermion vertex algebras." Letters in Mathematical Physics 108.12 (2018): 2543-2587.
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