Three-point Functions in Sine-Liouville Theory

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Abstract
We study the conjectured duality between sine-Liouville theory and the SL(2,R)/U(1) coset model by calculating the three-point functions in the latter explicitly. The evaluation of correlators boils down to that of a free-field theory with a certain number of insertion of screening operators. We prove that the winding number conservation is violated up to (+-)1 in three-point functions, which supports the conjecture of Fateev, Zamolodchikov and Zamolodchikov that in generic N-point correlators the winding number conservation is violated up to N-2 units. A new integral formula of Dotsenko-Fateev type is derived, using which we write down the generic three-point functions of tachyons explicitly. When the winding number is conserved, the resultant expression is shown to reproduce the correlators in the coset model correctly, including the group-theoretical factor. As an application, we also study the superstring theory on linear dilaton background which is described by super-Liouville theory. We obtain the three-point amplitude of tachyons in which the winding number conservation is violated.

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