A proof of the fusion rules theorem

Abstract

We prove that the space of intertwining operators associated with certain admissible modules over vertex operator algebras is isomorphic to a quotient of the vector space of conformal blocks on a three-pointed rational curve defined by the same data. This provides a new proof and alternative version of Frenkel and Zhu's fusion rules theorem in terms of the dimension of certain bimodules over Zhu's algebra, without the assumption of rationality.

Cited by in corpus (2)

• Twisted restricted conformal blocks of vertex operator algebras I: $g$-twisted correlation functions and fusion rules
• Bimodules over twisted Zhu algebras and twisted fusion rules theorem for vertex operator algebras