We now move to a different corner in the pentagon in Figure 7.1 and turn to the construction of type IIA orientifold compactifications down to four dimensions. The use of D-branes and their properties is crucial in these constructions, and provides a beautiful geometrical picture of the resulting 4d theories; gauge symmetries arise from overlapping D-branes, while charged chiral fermions arise from intersections among D-branes. The models are dubbed intersecting brane models and provide simple realizations of particle physics models in string theory.

Type II on CY and orientifolding

We now step back to Section 7.2 and consider the 4d compactification of type II theories on CY manifolds. They lead to 4d N =2 theories and are not suitable for particle physics model building, although some of their properties, like mirror symmetry, permeate the analysis of more realistic setups. We describe the introduction of orientifold projections truncating the supersymmetry to 4d N =1. These CY orientifolds provide the closed string sector of the compactifications in this and the next chapter, which contain sectors of Dbranes (to achieve RR tadpole cancellation) realizing non-trivial chiral gauge theories on their worldvolume.

Calabi–Yau compactification of type II string theories

Recall the general properties of KK compactification on CY manifolds from Section 7.2. Type IIA and IIB theories have two 10d gravitinos, so their CY compactifications contain two 4d gravitinos and correspond to 4d N =2 supersymmetric vacua.