On string theory in AdS_3 backgrounds

TL;DR

This paper reviews string theory formulations in AdS_3 backgrounds, focusing on the SL(2,R) and SL(2,C)/SU(2) WZW models, addressing key issues like unitarity, modular invariance, and correlation functions.

Contribution

It provides a detailed analysis of the fundamental issues in string theory on AdS_3 and explores methods to clarify problems related to unitarity and modular invariance.

Findings

Analysis of unitarity and modular invariance in SL(2,R) WZW model

Calculation of correlation functions in SL(2,C)/SU(2) WZW model

Discussion of approaches to resolve fundamental issues

Abstract

We discuss the string theory on AdS_3. In the first half of this talk, we review the SL(2,R) and the SL(2,C)/SU(2) WZW models which describe the strings on the Lorentzian and Euclidean AdS_3 without RR backgrounds, respectively. An emphasis is put on the fundamental issues such as the unitarity, the modular invariance and the closure of the OPE. In the second half, we discuss some attempts at clarifying such problems. In particular, we discuss the modular invariance of the SL(2,R) WZW model and the calculation of the correlation functions of the SL(2,C)/SU(2) WZW model using the path-integral approach.