We consider the phenomenological consequences of fixing compactification moduli. In the simplest Kachru-Kallosh-Linde-Trivedi constructions, stabilization of internal dimensions is rather soft: weak scale masses for moduli are generated, and are of order $m_{\sigma }\sim m_{3/2}$. 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 Kallosh-Linde 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 to 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 [$\sim \mathcal{O}(100)\mathrm{TeV}$], resolving the cosmological gravitino problem and problems with tachyonic staus in AMSB models.

• Received 15 November 2011

DOI:https://doi.org/10.1103/PhysRevD.85.066005