Coset conformal field theory

Abstract

We give the procedure that finds the unitary irreducible highest weight representations of the general G/H coset conformal field theory using the concept of the null vector for the Kac-Moody theory. According to this procedure we construct the unitary irreducible representations for SU(2)$_K\otimes$ SU(2)$_L$/ Su(2)$_{K+L}$ CFT. We show explicitly a one-to-one correspondence between out representations and the generalized Feigin-Fuchs representations of Virasoro algebra with central charge $c>1$. As a by product the fusion rules of these theories was obtained. And finally we have shown that the dynamics of the coset conformal field theory can be realized from the dynamics of their isometry and isotropy groups. This expands the equivalence between coset representations and the Feigin-Fuchs representations to the dynamics.