The Stoyanovsky-Ribault-Teschner Map and String Scattering Amplitudes

TL;DR

This paper explores the deep correspondence between SL(2,C) WZNW models and Liouville theory, applying it to string theory in curved backgrounds, analyzing divergences, pole structures, and scattering amplitudes, and connecting with the FZZ conjecture and tachyon condensation.

Contribution

It extends the Stoyanovsky-Ribault-Teschner map to string theory applications, analyzing divergences, pole structures, and scattering amplitudes, and relates these to the FZZ conjecture and tachyon dynamics.

Findings

Divergences in AdS_3 worldsheet instantons relate to dual screening operators in Liouville theory.

Pole structures in 2D black hole correlators have holographic interpretations in Little String Theory.

Winding number violating amplitudes connect to Liouville observables, and the k->0 limit aligns with the FZZ conjecture.

Abstract

Recently, Ribault and Teschner pointed out the existence of a one-to-one correspondence between N-point correlation functions for the SL(2,C)_k/SU(2) WZNW model on the sphere and certain set of 2N-2-point correlation functions in Liouville field theory. This result is based on a seminal work by Stoyanovsky. Here, we discuss the implications of this correspondence focusing on its application to string theory on curved backgrounds. For instance, we analyze how the divergences corresponding to worldsheet instantons in AdS_3 can be understood as arising from the insertion of the dual screening operator in the Liouville theory side. We also study the pole structure of N-point functions in the 2D Euclidean black hole and its holographic meaning in terms of the Little String Theory. This enables us to interpret the correspondence between CFTs as encoding a LSZ-type reduction procedure. Furthermore, we discuss the scattering amplitudes violating the winding number conservation in those backgrounds and provide a formula connecting such amplitudes with observables in Liouville field theory. Finally, we study the WZNW correlation functions in the limit k -> 0 and show that, at the point k=0, the Stoyanovsky-Ribault-Teschner dictionary turns out to be in agreement with the FZZ conjecture at a particular point of the space of parameters where the Liouville central charge becomes c=-2. This result makes contact with recent studies on the dynamical tachyon condensation in closed string theory.