Remarks on free field realization of SL(2,R)/U(1) x U(1) WZNW model
  Free field representations of vertex algebra in SL(2,R)/U(1) x U(1) WZNW model are constructed by considering a twisted version of the Bershadsky-Kutasov free field description of discrete states in the two-dimensional black hole CFT. These correspond to conjugate representations describing primary states in the model on SL(2,R)/U(1) x U(1). A particular evaluation of these leads to identities due to the spectral flow symmetry of sl(2)_k algebra.   The computation of correlation functions is discussed and, as an application, these are compared with analogous results known for the sine-Liouville theory. Exact agreement is observed between both analytic structures. 
Gaston Giribet, Daniel Lopez-Fogliani