KKLT type models with moduli-mixing superpotential

We study KKLT type models with moduli-mixing superpotential. In several string models, gauge kinetic functions are written as linear combinations of two or more moduli fields. Their gluino condensation generates moduli-mixing superpotential. We assume one of moduli fields is frozen already around the string scale. It is found that K\"ahler modulus can be stabilized at a realistic value without tuning 3-form fluxes because of gluino condensation on (non-)magnetized D-brane. Furthermore, we do not need to highly tune parameters in order to realize a weak gauge coupling and a large hierarchy between the gravitino mass and the Planck scale, when there exists non-perturbative effects on D3-brane. SUSY breaking patterns in our models have a rich structure. Also, some of our models have cosmologically important implications, e.g., on the overshooting problem and the destabilization problem due to finite temperature effects as well as the gravitino problem and the moduli problem.