Equivalence of BRST cohomologies for 2-d black hole and c=1 Liouville theory

TL;DR

This paper demonstrates the equivalence of BRST cohomologies between the 2D black hole model and the c=1 Liouville theory by constructing an explicit interpolating deformation, revealing their physical spectra are isomorphic.

Contribution

The authors explicitly construct a deformation interpolating BRST operators, establishing the isomorphism of cohomologies and spectra between the two models.

Findings

BRST cohomologies of black hole and c=1 Liouville are equivalent

Constructed an explicit deformation linking the models

Physical spectra are shown to be isomorphic

Abstract

We study the relation between the $SL(2,R)/U(1)$ black hole and the $c=1$ Liouville theory. A deformation, which interpolates the BRST operators of both models, is explicitly constructed. This interpolation is isomorphic, and the physical spectrum of the black hole is equivalent to that of the $c=1$ model tensored by a topological $U(1)/U(1)$ model. Some implications of the deformation are discussed.