HIGHER-DERIVATIVE GRAVITY IN STRING THEORY

We explicitly extract the structure of higher-derivative curvature-squ ared terms at genus 0 and 1 in the d=4 heterotic string effective acti on compactified on symmetric orbifolds by computing on-shell S-matrix superstring amplitudes. In particular, this is done within the context of calculating the graviton 4-point amplitude. We also discuss the mo duli-dependent gravitational threshold corrections to the coupling ass ociated with the CP even quadratic curvature terms.