We show that type I string theory compactified in four dimensions in the presence of constant internal magnetic fields possesses N=1 supersymmetric vacua, in which all Kahler class and complex structure closed string moduli are fixed. Furthermore, their values can be made arbitrarily large by a suitable tuning of the quantized magnetic fluxes. We present an explicit example for the toroidal compactification on T^6 and discuss Calabi-Yau generalizations. This mechanism can be complementary to other stabilization methods using closed string fluxes but has the advantage of having an exact string description and thus a validity away from the low-energy supergravity approximation. Moreover, it can be easily implemented in constructions of string models based on intersecting D-branes

Stabilization of closed string moduli in toroidal orientifold compactifications of type IIB string theory are studied using constant internal magnetic fields on D-branes and 3-form fluxes that preserve N = 1 supersymmetry in four dimensions. Our analysis corrects and extends previous work by us, and indicates that charged scalar VEV's need to be turned on, in addition to the fluxes, in order to construct a consistent supersymmetric model. As an explicit example, we first show the stabilization of all Kähler class and complex structure moduli by turning on magnetic fluxes on different sets of D9-branes that wrap the internal space T 6 in a compactified type I string theory, when a charged scalar on one of these branes acquires a non-zero VEV. The latter can also be determined by adding extra magnetized branes, as we demonstrate in a subsequent example. In a different model with magnetized D7-branes, in a IIB orientifold on T 6 /Z 2 , we show the stabilization of all the closed string moduli, including the axion-dilaton at weak string coupling g s , by turning on appropriate closed string 3-form fluxes. * Ignatios.Antoniadis@cern.ch † kumar@iopb.res.in ‡ Tristan.Maillard@cpht.polytechnique.fr arXiv:hep-th