Flux compactifications in string theory: a comprehensive review
Mariana Graña
TL;DR
Flux compactifications provide a perturbative mechanism to stabilize many or all moduli in string theory by turning on NS and RR fluxes, D-branes, and orientifolds in Calabi–Yau or SU(3)/SU(3) structure manifolds. The paper surveys the formalism (including generalized complex geometry), the resulting four-dimensional effective theories, and the conditions (Bianchi identities, tadpoles) that constrain consistent solutions. It catalogs how fluxes generate superpotentials and potentials that fix complex structure, dilaton, and in some cases Kähler moduli, with non-perturbative effects (gaugino condensation, D-brane instantons) essential for full stabilization and the possible realization of de Sitter vacua via uplifting. The work also discusses statistical distributions of flux vacua, the role of warping and backreaction, and key no-go theorems that shape the landscape of viable four-dimensional theories. Overall, flux compactifications illuminate how string theory can realize realistic vacua, while highlighting ongoing theoretical challenges in backreaction, moduli stabilization robustness, and cosmological constant problem.
Abstract
We present a pedagogical overview of flux compactifications in string theory, from the basic ideas to the most recent developments. We concentrate 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 analyze the resulting four-dimensional effective theories, as well as some of its perturbative and non-perturbative corrections, focusing on moduli stabilization. Finally, we briefly review statistical studies of flux backgrounds.