Abstract: 
H_{3}^{+} model describes strings on 3 dimensional Antide Sitter
space, and it is known that Npoint function of H_{3}^{+} model can be
reduced to (2N2)point function of a more tractable theory, i.e.,
Liouville field theory. Utilizing path integral formulation we rederive
this relation in a quite simple manner. Since the derivation is so
simple and intuitive, we can apply this method to other interesting
cases, such as, higher genus case, supersymmetric case, and gauged model
case. In particular, gauged model case is quite important because we can
show that the correspondence is equivalent to the Tduality (FZZ
duality) between Witten's cigar model and SineLiouville theory proposed
by Fateev, Zamolodchikov, and Zamolodchikov.
