A Chiral N=1 Type I Vacuum in Four Dimensions and Its Heterotic Dual

In this paper we consider Type I string theory compactified on a Z_7 orbifold. The model has N=1 supersymmetry, a U(4) \otimes U(4) \otimes U(4) \otimes SO(8) gauge group, and chiral matter. There are only D9-branes (for which we discuss tadpole cancellation conditions) in this model corresponding to a perturbative heterotic description in a certain region of the moduli space. We construct the heterotic dual, match the perturbative type I and heterotic tree-level massless spectra via giving certain scalars appropriate vevs, and point out the crucial role of the perturbative superpotential (on the heterotic side) for this matching. The relevant couplings in this superpotential turn out to be non-renormalizable (unlike the Z-orbifold case discussed in Ref [1], where Yukawa couplings sufficed for duality matching). We also discuss the role of the 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. We point out possible generalizations of the Z_3 and Z_7 cases to include D5-branes which would help in understanding non-perturbative five-brane dynamics on the heterotic side.