Free field approach to string theory on AdS3

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. (C) 2001 Elsevier Science B.V. All rights reserved.