FZZ Algebra

TL;DR

This paper revisits the duality between Sine-Liouville theory and 2D black holes, demonstrating the consistency of dual dressings and exploring higher winding perturbations' roles in c=1 string theory.

Contribution

It introduces a unified approach to Sine-Liouville dressings, clarifies their relation to black hole operators, and links higher winding perturbations to higher-spin states in c=1 strings.

Findings

Consistent Sine-Liouville dressings with correlation functions

OPE of dressings yields black hole deformation operator

Higher winding perturbations relate to higher-spin states

Abstract

The duality between the Sine-Liouville conformal field theory and the two dimensional black hole is revisited by considering the two possible Sine-Liouville dressings together. We show that this choice is consistent with the structure of correlation functions, and that the OPE of the two dressings yields the black hole deformation operator. As an application of this approach, we investigate the role of higher winding perturbations in the context of c=1 strings, where we argue that they are related to higher-spin discrete states that generalize the 2d black hole operator.