Factorization of Correlation Functions in Coset Conformal Field Theories

We use the conformal Ward identities to study the structure of correlation functions in coset conformal field theories. For a large class of primary fields of arbitrary g/h theory a factorization anzatz is found.The corresponding correlation functions are explicitly expressed in terms of correlation functions of two independent WZNW theories for g and h. Coset theories is an important subclass of two-dimensional conformal invariant QFT's.(For a review see [1].) The g/h coset theory is based on the Virasoro algebra generated by [2, 3] K(m) = L g (m) − L h (m), m ∈ Z. (1) The operator L g (m) is a conformal generator of the Wess-Zumino-Novikov-Witten (WZNW) theory [4-6] for the Lie algebra g and h ⊂ g. In this paper we study the connection between the coset and WZNW theories which follows from (1) at the level of correlation functions and primary fields. In the case of su(2)/u(1) correlation functions of primary fields may be written in terms of correlation functions of the independent WZNW theories for su(2) and u(1) [7].Correlation functions of the g/u(1) d , d = 1. .. rank g, cosets [8] have a similar structure.In [9] some correlation functions of minimal models were expressed in terms of correlation functions of two WZNW theories.