Liouville Theory Perturbed by the Black - Hole Mass Operator

We discuss the properties of the Liouville theory coupled to the c = 1 matter when perturbed by an operator, the screening operator of the SL(2;R) current algebra, which is supposed to generate the mass of the two-dimensional black hole. Mimicking the standard KPZ scaling theory of the Liouville system perturbed by the cosmological constant operator, we develop a scaling theory of correlation functions as functions of the mass of the black hole. Contrary to the case of KPZ, the present theory does not have the c = 1 barrior and seems somewhat insensitive to the details of the matter content of the theory; the string succeptibility equals 1 independent of the matter central charge. It turns out that our scaling exponents agree with those of the deformed matrix model recently proposed by Jevicki and Yoneya. In this article we would like to discuss the behavior of the Liouville theory coupled to the c = 1 matter when it is perturbed by an operator V which generates a mass for the two-dimensional black hole. The black-hole mass operator is essentially the screening operator of the SL(2;R) current algebra [1] and has appeared in the study of the two-dimensional black hole based on the SL(2;R)/U(1) gauged WZW model [2]. If one uses the operator correspodence between the c = 1 Liouville and SL(2;R)/U(1) coset theories [3], the operator V is expressed as V = (∂X − i √ k′ k ∂φ) exp(− √