Rationality, quasirationality and finite \(W\)-algebras (Q1416903)

The authors analyse some of consequences that follow from the \(C_2\) condition of Zhu and show that every conformal field theory satisfying the \(C_2\) condition has only finitely many \(n\)-point functions. The authors also show that every such vertex operator algebra is a finite \(W\)-algebra and give a direct proof of the convergence of its characters as well as the finiteness of the fusion rules.