Stabilization of moduli by fluxes

One of the major problem appearing in compactifications of string theory, is the emergence of a continuous moduli space of string vacua. In order to get contact, not only to the standard model of particle physics, but also to (inflationary) cosmology, these moduli have to be fixed and if supersymmetry is broken only at fairly low energies, we have to understand the mechanism while preserving at least some supersymmetries. Moduli appear in two guises: the closed string or geometrical moduli, related to deformations of the size and shape of cycles of the internal manifold and open string moduli, related to un-fixed positions of wrapped branes. Fluxes provide a mechanism to lift both moduli. On one hand, fluxes cause a gravitational force which expands/contract a cycle that is parallel/perpendicular to the flux and these competing effects yield the stabilization at values related to the strength to the different fluxes. Note, if a given cycle is parallel or perpendicular to all fluxes, it is not stabilized and the supergravity potential has a run-away mode. On the other hand, fluxes couple also to the world volume action of branes producing a potential for the open string moduli. Since the open string moduli are compact, any potential has an extremum and gives a stabilization of these moduli.