Magnetic fluxes and moduli stabilization

TL;DR

This paper investigates stabilizing all closed string moduli in type IIB string theory compactifications using magnetic fluxes and 3-form fluxes, highlighting the necessity of charged scalar VEVs for consistent supersymmetric models.

Contribution

It extends previous work by demonstrating moduli stabilization with magnetic fluxes and scalar VEVs, providing explicit examples in type I and type IIB orientifold compactifications.

Findings

All Kahler and complex structure moduli can be stabilized with magnetic fluxes.

All closed string moduli, including the axion-dilaton, can be stabilized with 3-form fluxes.

Charged scalar VEVs are essential for consistent supersymmetric models.

Abstract

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 Kahler 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.