PERTURBATIVE COUPLINGS AND MODULAR-FORMS IN N=2 STRING MODELS WITH A WILSON LINE

We consider a class of four-parameter D = 4, N = 2 string models, name ly heterotic strings compactified on K3 x T-2 together with their dual type II partners on Calabi-Yau threefolds. With the help of generaliz ed modular forms (such as Siegel and Jacobi forms), we compute the per turbative prepotential and the perturbative Wilsonian gravitational co upling F-1 for each of the models in this class. We check heterotic/ty pe II duality for one of the models by relating the modular forms in t he heterotic description to the known instanton numbers in the type II description. We comment on the relation of our results to recent prop osals for closely related models. (C) 1997 Elsevier Science B.V.