GNXGL/GN+L CONFORMAL FIELD-THEORIES AND THEIR MODULAR INVARIANT PARTITION-FUNCTIONS

We study a Feigin-Fuchs construction of conformal field theories based on a $G \otimes G / G$ coset space, in terms of screened bosons and parafermions. This allows to get the formula for the conformal dimensions of primary operators. Lists of modular invariant partition functions for the $SU(3)$, $SO(5)$ and $G_2$ Wess-Zumino-Witten models are given. Besides the principal series of diagonal invariants, a complementary series exists for $SU(3)$ and $SO(5)$, which is due to the outer automorphism of the Kac-Moody algebra. Moreover, exceptional solutions appear at level 5, 9, 21 for $SU(3)$, at level 3, 7, 12 for $SO(5)$ and at level 3, 4 for $G_2$. From these modular invariants, those for the corresponding $G_N \otimes G_L / G_{N+L}$ models are constructed.