Supersymmetry Breaking due to Moduli Stabilization in String Theory
  We consider the phenomenological consequences of fixing compactification
moduli. In the simplest KKLT constructions, stabilization of internal
dimensions is rather soft: weak scale masses for moduli are generated, and are
of order m_\sigma ~ m_{3/2}. As a consequence one obtains a pattern of soft
supersymmetry breaking masses found in gravity and/or anomaly mediated
supersymmetry breaking (AMSB) models. These models may lead to destabilization
of internal dimensions in the early universe, unless the Hubble constant during
inflation is very small. Fortunately, strong stabilization of compactified
dimensions can be achieved by a proper choice of the superpotential (e.g in the
KL model with a racetrack superpotential). This allows for a solution of the
cosmological moduli problem and for a successful implementation of inflation in
supergravity. We show that strong moduli stabilization leads a very distinct
pattern of soft supersymmetry breaking masses. In general, we find that soft
scalar masses remain of order the gravitino mass, while gaugino masses nearly
vanish at the tree level, i.e. they are of order m_{3/2}^2/m_\sigma. Radiative
corrections generate contributions to gaugino masses reminiscent of AMSB models
and a decoupled spectrum of scalars reminiscent of split-supersymmetry. This
requires a relatively large gravitino mass ~ O(100) TeV, resolving the
cosmological gravitino problem and problems with tachyonic staus in AMSB
models.
