FZZ Scattering

TL;DR

This paper investigates the duality between 2D black hole and sine-Liouville conformal field theories through exact operator quantization of classical scattering, highlighting the role of duality in fixing quantum reflection coefficients.

Contribution

It introduces a novel approach linking classical scattering problems with quantum reflection coefficients via duality assumptions in conformal field theories.

Findings

Classical scattering does not uniquely determine quantum reflection coefficients.

Duality between theories constrains the reflection coefficient.

Relation to parafermionic symmetry methods is discussed.

Abstract

We study the duality between the two dimensional black hole and the sine-Liouville conformal field theories via exact operator quantization of a classical scattering problem. The ideas are first illustrated in Liouville theory, which is dual to itself under the interchange of the Liouville parameter b by 1/b. In both cases, a classical scattering problem does not determine uniquely the quantum reflection coefficient. The latter is only fixed by assuming that the dual scattering problem has the same reflection coefficient. We also discuss the relation of this approach to the method that exploits the parafermionic symmetry of the model to compute the reflection coefficient.