| Abstract: |
An exactly solvable model for 2d Euclidean black hole
(cigar) can be constructed by coset construction from H3+ model,
which describes strings on 3d Euclidean Anti-de Sitter space.
Some time ago it was conjectured by Fateev, Zamolodchikov, and
Zamolodchikov that this cigar model is dual to Sine-Liouville theory,
a theory on 2d cylinder deformed by a winding tachyon mode.
This duality is important since it is a strong-week duality
like T-duality, and moreover the relation is among a sigma model
and a theory with a non-trivial potential. In the first part of talk,
we obtain a relation between correlators of H3+ model and Liouville
theory and study its properties. Then we give a proof of the
FZZ-duality conjecture by making use of the H3+ Liouville relation.
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