On the connection between WZW and free field theories

A large class of primary fields which appear at any level of the WZW theories (of types AN, BN, CN, DN, E6, and E7) are shown to possess simple power-like four-point functions. As a consequence, these fields, which are in 1-1 correspondence with the center of the covering group, may be written as symmetrized products of level one fields. The latter are known to be related to free fermions (AN, BN, DN) or free bosons (AN, DN, E6, E7). Our results indicate that a relation to free field theory exists also for the case of CN. (orig.)