In Chapter 5 we showed that toroidal compactifications of superstrings can lead at low energies to 4d theories, albeit with too much supersymmetry to allow for chirality, an essential ingredient of particle physics. We will thus be interested in constructing more general classes of compactifications leading to chiral theories in 4d, an enterprise starting in this chapter and reaching until Chapter 12, and for which it is convenient to give an aerial view.

A road map for string compactifications

There are different options to achieve the construction of chiral 4d compactifications in string theory, summarized in Figure 7.1, and roughly classified according to the underlying 10d or 11d theory taken as starting point. In this book we will study in turn heterotic compactifications, type IIA orientifolds and type IIB orientifolds. In this chapter and Chapter 8 we describe different varieties of heterotic string compactifications, whose 4d effective action is studied in Chapter 9. We consider models in the geometric realm, using Calabi–Yau manifolds and toroidal orbifolds, and in the more abstract non-geometric conformal field theory (CFT) framework, using asymmetric orbifolds, free fermions, and Gepner constructions. In Chapter 10 we study type IIA orientifold constructions with gauge fields localized on D6-branes, and matter fields at their intersections. We consider explicit examples in toroidal orbifold compactifications, as well as Gepner constructions. Supersymmetric type IIA models with intersecting D6-branes are related to purely geometric compactifications of M-theory on manifolds with G2 holonomy, as we will also review.