String GUT scenarios with stabilized moduli

Abstract

Taking into account the recently proposed poly-instanton corrections to the superpotential and combining the racetrack with a Kachru-Kallosh-Linde-Trivedi, respectively, large volume scenario in an intricate manner, we show that we gain exponential control over the parameters in an effective superpotential. This allows us to dynamically stabilize moduli such that a conventional minimal supersymmetric standard model scenario with the string scale lowered to the grand unified theory scale is realized. Depending on the cycles wrapped by the minimal supersymmetric standard model branes, two different scenarios for the hierarchy of soft masses arise. The first one is a supergravity mediated model with ${M}_{3/2}\ensuremath{\simeq}1\text{ }\text{ }\mathrm{TeV}$ while the second one features mixed anomaly supergravity mediation with ${M}_{3/2}\ensuremath{\simeq}{10}^{10}\text{ }\text{ }\mathrm{GeV}$ and split supersymmetry. We also comment on dynamically lowering the scales such that the tree level cosmological constant is of the order $\ensuremath{\Lambda}=({10}^{\ensuremath{-}3}\text{ }\text{ }\mathrm{eV}{)}^{4}$.