We present an explicit calculation of the spectrum of a general class ofstring models, corresponding to Calabi-Yau flux compactifications withh_{1,2}>h_{1,1}>1 with leading perturbative and non-perturbative corrections,in which all geometric moduli are stabilised as in hep-th/0502058. The volumeis exponentially large, leading to a range of string scales from the Planckmass to the TeV scale, realising for the first time the large extra dimensionsscenario in string theory. We provide a general analysis of the relevance ofperturbative and non-perturbative effects and the regime of validity of theeffective field theory. We compute the spectrum in the moduli sector finding ahierarchy of masses depending on inverse powers of the volume. We also computesoft supersymmetry breaking terms for particles living on D3 and D7 branes. Wefind a hierarchy of soft terms corresponding to `volume dominated' F-termsupersymmetry breaking. F-terms for Kahler moduli dominate both those fordilaton and complex structure moduli and D-terms or other de Sitter liftingterms. This is the first class of string models in which soft supersymmetrybreaking terms are computed after fixing all geometric moduli. We outlineseveral possible applications of our results, both for cosmology andphenomenology and point out the differences with the less generic KKLT vacua.
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