Aspects of N=1 type I-heterotic duality in four dimensions

In this paper we discuss some aspects of N=1 type I-heterotic string duality in four dimensions. We consider a particular example of a (weak-weak) dual pair where on the type I side there are only D9-branes corresponding to the perturbative heterotic description in a certain region of the moduli space. We match the perturbative type I and heterotic tree-level massless spectra by giving certain scalars appropriate vevs, and point out the crucial role of the perturbative superpotential (on the heterotic side) for this matching. We also discuss the role of anomalous U(1) gauge symmetry present in both type I and heterotic models. In the perturbative regime we match the (tree-level) moduli spaces of these models. Since both type I and heterotic models can be treated perturbatively, we are able to discuss a dictionary that in generic models maps the type I description onto the heterotic one, and vice versa. Finally, we discuss possible directions to study perturbative quantum corrections to the moduli space, as well as outline ways to learn about the non-perturbative effects in both descriptions. (orig.)