Perturbative couplings and modular forms in N = 2 string models with a Wilson line Original Research Article

We consider a class of four-parameter D = 4, N = 2 string models, namely heterotic strings compactified on K3 × T2 together with their dual type II partners on Calabi-Yau threefolds. With the help of generalized modular forms (such as Siege] and Jacobi forms), we compute the perturbative prepotential and the perturbative Wilsonian gravitational coupling F1 for each of the models in this class. We check heterotic/type II duality for one of the models by relating the modular forms in the heterotic description to the known instanton numbers in the type II description. We comment on the relation of our results to recent proposals for closely related models.