Strings inAdS3and theSL(2,R)WZW model. III. Correlation functions

We consider correlation functions for string theory on ${\mathrm{AdS}}_3.$ We analyze their singularities and we provide a physical interpretation for them. We explain which worldsheet correlation functions have a sensible physical interpretation in terms of the boundary theory. We consider the operator product expansion of the four-point function and we find that it factorizes only if a certain condition is obeyed. We explain that this is the correct physical result. We compute correlation functions involving spectral flowed operators and we derive a constraint on the amount of winding violation.