Free field realization of superstring theory on AdS3

The Coulomb gas representation of expectation values in SU(2) conformal field theory developed by Dotsenko is extended to the SL(2,R) WZW model and applied to bosonic string theory on AdS3 and to Type II superstrings on AdS3 x N. The spectral flow symmetry is included in the free field realization of vertex operators creating superstring states of both Ramond and Neveu-Schwarz sectors. Conjugate representations for these operators are constructed and a background charge prescription is designed to compute correlation functions. Two and three point functions of bosonic and fermionic string states in arbitrary winding sectors are calculated. Scattering amplitudes that violate winding number conservation are also discussed.Comment: 40 pages, typos corrected, references added, minor changes in presentation and details completed in the calculation of the R sector 2-point function. Version to appear in JHE