Higher-derivative gravity in string theory

We explicitly extract the structure of higher-derivative curvature-squared terms at genus 0 and 1 in the d = 4 heterotic string effective action 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 moduli-dependent gravitational threshold corrections to the coupling associated with the CP even quadratic curvature terms