Comments on sine-Liouville correlation functions: A FZZ-like dual for the 2D black hole

GASTON GIRIBET; MATIAS LEONI-OLIVERA

Praga, Republica Checa

Congreso; International Colloquium on Integrable Systems and Quantum symmetries (ISQS-16); 2007

We further investigate the duality between string theory formulated on a curved exact background (the two dimensional black hole) and string theory in flat tachyonic backgrounds. We generalize previous results on this subject by proving a twisted version of the Fateev-Zamolodchikov-Zamolodchikov conjecture. The duality is shown to hold at the level of $N$-point correlation functions on the sphere topology, and it connects tree-level string amplitudes in the euclidean version of the 2D black hole to correlation functions in a 2D non-linear $sigma $-model in flat space but in presence of a tachyon potential and a linear dilaton. This CFT corresponds to the perturbed 2D quantum gravity coupled to $c