4-D Chiral N=1 Type I Vacua With And Without D5-Branes

TL;DR

This paper explores compactifications of type I string theory on Abelian orbifolds, analyzing tadpole cancellation, dual heterotic models, and specific examples with D9- and D5-branes, revealing new insights into chiral vacua and gauge structures.

Contribution

It provides a detailed analysis of tadpole conditions and dualities for type I orbifold compactifications with D-branes, including explicit models with chiral matter and gauge groups.

Findings

Constructed explicit N=1 supersymmetric models with chiral matter.

Analyzed heterotic duals with extra twisted states and blow-up modes.

Identified conditions for tadpole cancellation in D9- and D5-brane setups.

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 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 I-heterotic (tree-level) duality matching. We illustrate these issues on a particular example of Z_3 \otimes Z_3 orbifold type I model (and its heterotic dual). The model has N=1 supersymmetry, U(4)^3 \otimes 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)\otimes U(6)\otimes U(4)]^2 gauge group, and chiral matter. This would correspond to a non-perturbative chiral vacuum from the heterotic point of view.