Large-volume flux compactifications: moduli spectrum and D3/D7 soft supersymmetry breaking

Abstract

We present an explicit calculation of the spectrum of a general class of string models, corresponding to Calabi-Yau flux compactifications with h 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 volume is exponentially large, leading to a range of string scales from the Planck mass to the TeV scale, realising for the first time the large extra dimensions scenario in string theory. We provide a general analysis of the relevance of perturbative and non-perturbative effects and the regime of validity of the effective field theory. We compute the spectrum in the moduli sector finding a hierarchy of masses depending on inverse powers of the volume. We also compute soft supersymmetry breaking terms for particles living on D3 and D7 branes. We find a hierarchy of soft terms corresponding to 'volume dominated' F-term supersymmetry breaking. Fterms for Kähler moduli dominate both those for dilaton and complex structure moduli and D-terms or other de Sitter lifting terms. This is the first class of string models in which soft supersymmetry breaking terms are computed after fixing all geometric moduli. We outline several possible applications of our results, both for cosmology and phenomenology and point out the differences with the less generic KKLT vacua.

Kähler moduli inflation

“…The flat directions have their origins in the no-scale property of the Kähler potential and are generic for IIB Kähler moduli, as is the appearance of instanton-generated nonperturbative superpotentials. The scenario is embedded in the exponentially large volume compactifications of [13,14] and requires h 2,1 > h 1,1 and h 1,1 > 2. This last requirement is necessary to ensure that the volume is stabilised during inflation.…”

“…The necessary volumes of O(10 5 − 10 7 ) in string units can be obtained by natural choices of the exponential parameters a i (a ∼ 2π 3 in the simplest cases) [14].…”

“…This field is so light, with m << 10 −300 GeV [14] both during and after inflation, that it will not play a role in the cosmological evolution.…”

“…We now embed the above in reasonably explicit IIB flux compactifications 3 and in particular in the moduli stabilisation mechanism of [13,14]. (For other recent work on perturbative corrections in IIB flux compactifications see [18,19,20,21,22]).…”

“…If the latter, we must replace a i → a i g s and ξ → ξg −3/2 s in (9) and (10) -the physics is of course the same. As we work in the moduli stabilisaton framework of [13,14] we anticipate that at the minimum we will have τ 1 >> τ i and V >> 1. The resulting scalar potential is…”