  Some of the consequences that follow from the C_2 condition of Zhu are
analysed. In particular it is shown that every conformal field theory
satisfying the C_2 condition has only finitely many n-point functions, and this
result is used to prove a version of a conjecture of Nahm, namely that every
representation of such a conformal field theory is quasirational. We also show
that every such vertex operator algebra is a finite W-algebra, and we give a
direct proof of the convergence of its characters as well as the finiteness of
the fusion rules.
