String correlators in AdS$_3$ from FZZ duality

TL;DR

This paper computes correlation functions in sine-Liouville theory using FZZ duality, connecting to Liouville theory and AdS3 string scattering, providing new explicit formulas and insights into spectral flow effects.

Contribution

It presents the first direct three-point function calculation in sine-Liouville theory and expresses N-point functions via Liouville correlators, advancing understanding of AdS3 string dynamics.

Findings

Explicit three-point function in sine-Liouville theory derived.

N-point functions expressed in terms of Liouville correlators.

Insights into spectral flow effects on AdS3 string scattering.

Abstract

Motivated by recent works in which the FZZ duality plays an important role, we revisit the computation of correlation functions in the sine-Liouville field theory. We present a direct computation of the three-point function, the simplest to the best of our knowledge, and give expressions for the $N$-point functions in terms of integrated Liouville theory correlators. This leads us to discuss the relation to the $H^+_3$ WZW-Liouville correspondence, especially in the case in which spectral flow is taken into account. We explain how these results can be used to study scattering amplitudes of winding string states in AdS$_3$.