Free Field Appoach to String Theory on AdS_3

TL;DR

This paper presents a free field approach to calculating correlation functions in the SL(2,C)/SU(2) WZW model, simplifying the process by reducing it to a free theory and accurately reproducing known results.

Contribution

It introduces a novel free field prescription for correlation functions in the Euclidean AdS_3 WZW model, including a method to handle zero-mode integration.

Findings

Correctly reproduces known two- and three-point functions

Derives some four-point functions using KZ equations

Provides a simplified calculation method for correlation functions

Abstract

We discuss the correlation functions of the SL(2,C)/SU(2) WZW model, or the CFT on the Euclidean AdS_3. We argue that their calculation is reduced to that of a free theory by taking into account the renormalization and integrating out a certain zero-mode, which is an analog of the zero-mode integration in Liouville theory. Based on the resultant free field picture, we give a simple prescription for calculating the correlation functions. The known exact two- and three-point functions of generic primary fields are correctly obtained, including numerical factors. We also obtain some four-point functions of primaries by solving the Knizhnik-Zamolodchikov equation, and verify that our prescription indeed gives them.