c=1 Liouville Theory Perturbed by the Black-Hole Mass operator

TL;DR

This paper develops a scaling theory for Liouville theory coupled to c=1 matter perturbed by a black-hole mass operator, revealing insensitivity to matter details and agreement with a deformed matrix model.

Contribution

It introduces a novel scaling framework for Liouville theory with black-hole mass perturbation, showing independence from matter content and matching matrix model predictions.

Findings

String susceptibility equals 1 regardless of matter central charge.

Scaling exponents match those of the recent deformed matrix model.

The theory does not exhibit the c=1 barrier typical in similar models.

Abstract

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 delatils 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 proposed recently by Jevicki and Yoneya.