Path Integral Approach to String Theory on AdS_3

TL;DR

This paper employs the path integral method to derive correlation functions in string theory on Euclidean AdS_3, matching known bootstrap results and connecting to supergravity in the semi-classical limit.

Contribution

It provides closed-form expressions for two- and three-point functions in the SL(2,C)/SU(2) WZW model using the path integral approach, aligning with previous bootstrap results.

Findings

Derived explicit two- and three-point functions

Results match bootstrap approach after normalization

Supergravity results obtained in semi-classical limit

Abstract

Using the path integral approach, we discuss the correlation functions of the $SL(2,\bfC)/SU(2)$ WZW model, which corresponds to the string theory on the Euclidean $AdS_3$. We obtain the two- and three-point functions for generic primary fields in closed forms. By an appropriate change of the normalization of the primary fields, our results coincide with those by Teschner, which were obtained by using the bootstrap approach. The supergravity results are also obtained in the semi-classical limit.