In all string compactifications studied in previous chapters, the massless spectrum contains a large number of moduli, including the dilaton and the CY geometric moduli. These are problematic, as they couple to matter particles and easily lead to deviations from universality of gravitational interactions (fifth forces), which have not been observed experimentally. Therefore, any serious attempt to reproduce realistic string models of particle physics and/or cosmology, must address the issue of moduli stabilization; namely, the generation of a scalar potential fixing the vevs of the moduli fields and giving them large enough masses to overcome such phenomenological problems. In this chapter we review a very general and systematic mechanism to fix large numbers of (or even all) moduli. It is based on a generalization of the simplest compactification ansatz, allowing for non-trivial backgrounds for additional 10d fields. Most prominently, the compactifications include non-trivial fluxes for the field strength tensor of the diverse p-form fields in the 10d theory. Application of string dualities to these motivates additional possible backgrounds, termed geometric and non-geometric fluxes. Compactifications including field strength fluxes, or their generalizations, are thus known as “flux compactifications.” This chapter focuses on their definition and impact on moduli stabilization, while their role in SUSY breaking is further explored in Chapter 15.

Type IIB with 3-form fluxes

A prototypical class of flux compactifications is obtained from type IIB (orientifolds) on CY geometries with non-trivial fluxes for the NSNS and RR 3-form field strengths (and their F-theory generalization, which we briefly touch upon).