Four-dimensional chiral N = 1 type I vacua with and without D5-branes

Abstract

In this paper we consider compactifications of type I strings on Abelian orbifolds. We discuss the tadpole cancellation conditions for the general case with D9-branes only. Such compactifications have (perturbative) heterotic duals which are also realized as orbifolds (with non-standard embedding of the gauge connection). The latter have extra twisted states that become massive once orbifold singularities are blown up. This is due to the presence of a perturbative heterotic superpotential with couplings between the extra twisted states, the orbifold blow-up modes, and (sometimes) untwisted matter fields. Anomalous U(1) (generically present in such models) also plays an important role in type 1-heterotic (tree-level) duality matching. We illustrate these issues on a particular example of Z 3 ⊗ Z 3 orbifold type I model (and its heterotic dual). The model has N = 1 supersymmetry, U(4) 3 ⊗ SO(8) gauge group, and chiral matter. We also consider compactifications of type I strings on Abelian orbifolds with both D9- and D5-branes. We discuss tadpole cancellation conditions for a certain class of such models. We illustrate the model building by considering a particular example of type I theory compactified on Z 6 orbifold. The model has N = 1 supersymmetry, [ U(6) ⊗ U(6) ⊗ U(4)] 2 gauge group, and chiral matter. This would correspond to a non-perturbative chiral vacuum from the heterotic point of view.