Abstract
We develop a general method of solving non-trivial conformal field theories by coset imbeddings into free boson models. In particular, we consider Z N parafermion models represented by the coset model constructions su( N 1)⊕ su( N) 1/ su( N) 2, and bosonize the su( N) 1 models. The calculation of correlation functions of these parafermion theories is formulated so that detailed information from the diagonal su( N) 2 theory is not required. A differential equation for the four-point functionof order operators σ 1 is derived as an example. We also derive differential equations with respect to the modular parameter τ for the parafermion characters in terms of the su( N) 1 characters only. In particular, the equations for the Z 2 and Z 3 characters are first and second order respectively.
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