Free field representation of parafermions and related coset models

A construction is proposed for representation of the operator algebra of parafermions in terms of free boson fields with energy–momentum tensor as in the Goddard–Kent–Olive construction. The boson construction leads to expressions of Dotsenko–Fateev type for conformal blocks on the sphere. Asymmetric models of $G\times G/G$ type are discussed. Multiloop calculations in such theories are briefly considered.