One-loop amplitudes of winding strings in AdS$_3$ and the Coulomb gas approach

TL;DR

This paper presents a Coulomb gas approach to compute scattering amplitudes of winding strings in AdS3 using the SL(2,R) WZW model, enhancing previous free-field methods and clarifying the WZW-Liouville correspondence.

Contribution

It introduces a refined Coulomb gas realization for n-point functions in the SL(2,R) WZW model suitable for tree-level and one-loop string amplitude calculations.

Findings

Provides a method to compute winding string scattering amplitudes in AdS3.

Clarifies the WZW-Liouville correspondence in the context of string theory.

Enhances previous free-field realizations with a more manifest approach.

Abstract

We discuss a Coulomb gas realization of $n$-point correlation functions in the $SL(2,\mathbb{R})$ Wess-Zumino-Witten (WZW) model that is suitable to compute scattering amplitudes of winding strings in 3-dimensional Anti-de Sitter space at tree-level and one-loop. This is a refined version of previously proposed free-field realizations that, among other features, accomplishes to make the $H_3^+$ WZW-Liouville correspondence manifest.