Moduli stabilization and the pattern of soft SUSY breaking terms(SUMMER INSTITUTE 2005)

In string compactification preserving N=1 SUSY, moduli fields are plausible candidates for the messenger of SUSY breaking at low energy scales. In a scenario that moduli-mediated SUSY breaking is significant, the pattern of soft SUSY breaking terms depends crucially on how the light moduli with mass m \lesssim O(8\pi^2 m_{3/2}) are stabilized. We discuss the correspondence between the pattern of soft terms and the stabilization mechanism of light moduli within the framework of 4D effective supergravity which is generalized to include a SUSY-breaking uplifting potential which might be necessary to get the phenomenologically viable de-Sitter (or Minkowski) vacuum. In some special case, light moduli can be stabilized by controllably small perturbative corrections to the K\"ahler potential, yielding the soft terms dominated by the moduli-mediated contribution. In more generic situation, light moduli are stabilized by non-perturbative effects encoded in the superpotential and a quite different pattern of soft terms emerges: the anomaly-mediated soft terms become comparable to the moduli-mediated ones. Such mixed moduli-anomaly mediated soft terms lead to low energy superparticle masses qualitatively different from those of other mediation models such as mSUGRA scenario, gauge-mediation, and anomaly-mediation.