Strings in AdS3 and the SL(2,R) WZW model.: I:: The spectrum

In this paper we study the spectrum of bosonic string theory on AdS(3). We study classical solutions of the SL(2,R) WZW model, including solutions for long strings with nonzero winding number. We show that the model has a symmetry relating string configurations with different winding numbers. We then study the Hilbert space of the WZW model, including all states related by the above symmetry. This leads to a precise description of long strings. We prove a no-ghost theorem for all the representations that are involved and discuss the scattering of the long string. (C) 2001 American Institute of Physics.