Flux compactifications and generalized geometries**This is an abridged version of Physics Reports, M Graña, ‘Flux compactifications in string theory: A comprehensive review’ 423 91–158, Copyright (2006), reprinted with permission from Elsevier.

Abstract

Following the lectures given at CERN Winter School 2006, we present a pedagogical overview of flux compactifications and generalized geometries, concentrating on closed string fluxes in type II theories. We start by reviewing the supersymmetric flux configurations with maximally symmetric four-dimensional spaces. We then discuss the no-go theorems (and their evasion) for compactifications with fluxes. We analyse the resulting four-dimensional effective theories for Calabi–Yau and Calabi–Yau orientifold compactifications, concentrating on the flux-induced superpotentials. We discuss the generic mechanism of moduli stabilization and illustrate with two examples: the conifold in IIB and a torus in IIA. We finish by studying the effective action and flux vacua for generalized geometries in the context of generalized complex geometry.