Large-Volume Flux Compactifications: Moduli Spectrum and D3/D7 Soft Supersymmetry Breaking

TL;DR

The paper analyzes a large class of Type IIB flux compactifications with Calabi–Yau geometries where all geometric moduli are stabilised at exponentially large volumes. By including leading perturbative α' corrections alongside non-perturbative effects, the authors demonstrate a robust large-volume minimum with a hierarchy of scales, and they compute the moduli spectrum and soft SUSY breaking terms for matter on D3 and D7 branes. A volume-dominated F-term breaking pattern emerges, with the volume modulus setting the SUSY-breaking scale and other moduli gaining masses suppressed by powers of the volume; D-terms and uplift mechanisms are shown to provide subleading contributions. The results distinguish these vacua from KKLT and have wide-ranging implications for cosmology and phenomenology, including possible connections to TeV-scale soft terms and moduli-driven cosmology.

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. F-terms for Kahler 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.

Figures (2)

• Figure 1: $\ln (V)$ for ${\mathbb{P}}^4_{[1,1,1,6,9]}$ in the large volume limit, as a function of the divisors $\tau_4$ and $\tau_5$. The void channel corresponds to the region where $V$ becomes negative and $\ln (V)$ undefined. As $V \to 0$ at infinite volume, this immediately shows that a large-volume minimum must exist.
• Figure 2: A Swiss cheese picture of a Calabi-Yau. There is one pair of large 2- and 4-cycles - increasing the cycle volume increases the overall volume. The other pairs are such that increasing the cycle volume decreases the overall volume.