Abstract: 
An exactly solvable model for 2d Euclidean black hole
(cigar) can be constructed by coset construction from H_{3}^{+} model,
which describes strings on 3d Euclidean Antide Sitter space.
Some time ago it was conjectured by Fateev, Zamolodchikov, and
Zamolodchikov that this cigar model is dual to SineLiouville theory,
a theory on 2d cylinder deformed by a winding tachyon mode.
This duality is important since it is a strongweek duality
like Tduality, and moreover the relation is among a sigma model
and a theory with a nontrivial potential. In the first part of talk,
we obtain a relation between correlators of H_{3}^{+} model and Liouville
theory and study its properties. Then we give a proof of the
FZZduality conjecture by making use of the H_{3}^{+} Liouville relation.
