Recently an interesting relation has been discovered between conformal blocks of affine $SL(2)$ and Virasoro algebras. By using it, the correlation functions of $H_3^+$ WZW model on the sphere have been related to those in Liouville theory by Ribault and Teschner. I will explain how to generalize this correspondence to disc (or the upper half plane) and determine the disc correlators in $H_3^+$ in terms of those of Liouville theory.

SPhT