2-POINT AND 3-POINT FUNCTIONS IN LIOUVILLE THEORY

Based on our generalization of the Goulian-Li continuation in the powe r of the 2D cosmological term we construct the two- and three-point co rrelation functions for Liouville exponentials with generic real coeff icients. As a strong argument in favour of the procedure we prove the Liouville equation of motion on the level of three-point functions. Th e analytical structure of the correlation functions as well as some of its consequences for string theory are discussed. This includes a con jecture on the mass shell condition for excitations of noncritical str ings. We also make a comment concerning the correlation functions of t he Liouville field itself.