Scalar field theory limits of bosonic string amplitudes

We describe in detail the techniques needed to compute scattering amplitude s for colored scalars from the infinite tension limit of bosonic string the ory, up to two loops. These techniques apply both to cubic and quartic inte ractions, and to planar as well as non-planar diagrams. The resulting field theories are naturally defined in the space-time dimension in which they a re renormalizable. With a careful analysis of string moduli space in the Sc hottky representation we determine the region of integration for the moduli , which plays a crucial role in the derivation of the correct combinatorial and color factors for all diagrams. (C) 2000 Elsevier Science B.V. All rig hts reserved.