  Motivated by recent works in which the FZZ duality plays an important role,
we revisit the computation of correlation functions in the sine-Liouville field
theory. We present a direct computation of the three-point function, the
simplest to the best of our knowledge, and give expressions for the $N$-point
functions in terms of integrated Liouville theory correlators. This leads us to
discuss the relation to the $H^+_3$ WZW-Liouville correspondence, especially in
the case in which spectral flow is taken into account. We explain how these
results can be used to study scattering amplitudes of winding string states in
AdS$_3$.
