Fusion categories for affine vertex algebras at admissible levels

• Thomas Creutzig ^[1]
  1. [1] University of Alberta

     University of Alberta

     Canadá

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 25, Nº. 2, 2019
• Idioma: inglés
• DOI: 10.1007/s00029-019-0479-6
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• Resumen

  • The main result is that the category of ordinary modules of an affine vertex operator algebra of a simply laced Lie algebra at admissible level is rigid and thus a braided fusion category. If the level satisfies a certain coprime property then it is even a modular tensor category. In all cases open Hopf links coincide with the corresponding normalized S-matrix entries of torus one-point functions. This is interpreted as a Verlinde formula beyond rational vertex operator algebras. A preparatory Theorem is a convenient formula for the fusion rules of rational principal W-algebras of any type.