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.