A proof for string three-point functions in AdS 3

Abstract

Correlation functions of the SL(2,ℝ)-WZW model involving spectrally flowed vertex operators are notoriously difficult to compute. An explicit integral expression for the corresponding three-point functions was recently conjectured in [1]. In this paper, we provide a proof for this conjecture. For this, we extend the methods of [2] based on the so-called SL(2,ℝ) series identifications, which relate vertex operators belonging to different spectral flow sectors. We also highlight the role of holomorphic covering maps in this context. Our results constitute an important milestone for proving this instance of the AdS3/CFT2 holographic duality at finite ’t Hooft coupling.