Duality of string amplitudes in a curved background

We initiate a program to study the relationship between the target space, the spectrum and the scattering amplitudes in string theory. We consider scattering amplitudes following from string theory and quantum field theory on a curved target space, which is taken to be the $SU(2)$ group manifold, with special attention given to the duality between contributions from different channels. We give a simple example of the equivalence between amplitudes coming from string theory and quantum field theory, and compute the general form of a four-scalar field theoretical amplitude. The corresponding string theory calculation is performed for a special case, and we discuss how more general string theory amplitudes could be evaluated.