Recently, Ribault and Teschner pointed out the existence of a one-to-one
correspondence between N-point correlation functions for the SL(2,C)_k/SU(2)
WZNW model on the sphere and certain set of 2N-2-point correlation functions in
Liouville field theory. This result is based on a seminal work by Stoyanovsky.
Here, we discuss the implications of this correspondence focusing on its
application to string theory on curved backgrounds. For instance, we analyze
how the divergences corresponding to worldsheet instantons in AdS_3 can be
understood as arising from the insertion of the dual screening operator in the
Liouville theory side. We also study the pole structure of N-point functions in
the 2D Euclidean black hole and its holographic meaning in terms of the Little
String Theory. This enables us to interpret the correspondence between CFTs as
encoding a LSZ-type reduction procedure. Furthermore, we discuss the scattering
amplitudes violating the winding number conservation in those backgrounds and
provide a formula connecting such amplitudes with observables in Liouville
field theory. Finally, we study the WZNW correlation functions in the limit k
-> 0 and show that, at the point k=0, the Stoyanovsky-Ribault-Teschner
dictionary turns out to be in agreement with the FZZ conjecture at a particular
point of the space of parameters where the Liouville central charge becomes
c=-2. This result makes contact with recent studies on the dynamical tachyon
condensation in closed string theory.