Modularity of logarithmic parafermion vertex algebras - Auger, Jean; Creutzig, Thomas; Ridout, David (Letters in Mathematical Physics, 2018)
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.
CRIS-Team Scopus Importer:2024-06-24
Keywords: Conformal field theory; Coset constructions; Modular transformations; Parafermions; Vertex algebras