Moduli Corrections to Gauge and Gravitational Couplings in four dimensional Superstrings

We study one-loop, moduli-dependent corrections to gauge and gravitational couplings in supersymmetric vacua of the heterotic string. By exploiting their relation to the integrability condition for the associated CP-odd couplings, we derive general expressions for them, both for $(2,2)$ and $(2,0)$ models, in terms of tree level four-point functions in the internal $N=2$ superconformal theory. The $(2,2)$ case, in particular symmetric orbifolds, is discussed in detail.