On the effective description of large volume compactifications

Abstract

Abstract:We study the reliability of the Two-Step moduli stabilization in the type-IIB Large Volume Scenarios with matter and gauge interactions. The general analysis is based on a family of N = 1 Supergravity models with a factorizable Kähler invariant function, where the decoupling between two sets of fields without a mass hierarchy is easily understood. For the Large Volume Scenario particular analyses are performed for explicit models, one of such developed for the first time here, finding that the simplified version, where the Dilaton and Complex structure moduli are regarded as frozen by a previous stabilization, is a reliable supersymmetric description whenever the neglected fields stand at their leading F -flatness conditions and be neutral. The terms missed by the simplified approach are either suppressed by powers of the Calabi-Yau volume, or are higher order operators in the matter fields, and then irrelevant for the moduli stabilization procedure. Although the power of the volume suppressing such corrections depends on the particular model, up to the mass level it is independent of the modular weight for the matter fields. This at least for the models studied here but we give arguments to expect the same in general. These claims are checked through numerical examples. We discuss how the factorizable models present a context where despite the lack of a hierarchy with the supersymmetry breaking scale, the effective theory still has a supersymmetric description. This can be understood from the fact that it is possible to find vanishing solution for the auxiliary components of the fields being integrated out, independently of the remaining dynamics. Our results settle down the question on the reliability of the way the Dilaton and Complex structure are treated in type-IIB compactifications with large compact manifold volumina.

Anisotropic modulus stabilisation: strings at LHC scales with micron-sized extra dimensions

“…(2.3)). Of these, the S and the U -moduli can be stabilised at leading order in g s and α ′ if nonzero 3-form fluxes are present in the background geometry [5,35]. By contrast, the Kähler moduli T i remain unstabilised at leading semiclassical order.…”

A new class of de Sitter vacua in type IIB large volume compactifications

“…Under these circumstances (3.10) does not imply λ I = |W |, and generically, the complex structure moduli and the axio-dilaton are stabilised at the scale O max(e K λ 2 I , e K |W | 2 ) for each λ I . These moduli are then generically decoupled from the details of the Kähler moduli stabilisation [73][74][75].…”

“…The implications of this equation are again very important: the three-form fluxes can stabilise most of the fields in the complex structure and axiodilaton sector with squared masses of ∼ 1/V 2 min , but a consistent inclusion of the additional 5 The existence of run-away directions in the moduli space has since long been identified as a critical aspect of string compactifications [76]. A detailed analysis of the FIF I ∼ |W | 2 case is intricate: for comparatively small volumes and large supersymmetry breaking the various contributions to the potential become of similar magnitude and couplings between the axio-dilaton, complex structure and the Kähler moduli are all important [73,74]. Moreover, the applicability of the four-dimensional N = 1 supergravity as an effective description of the low-energy theory becomes questionable as the hierarchy between the compactification scale and the supersymmetry breaking scale decreases.…”

Effective upliftings in Large volume compactifications

“…Then, for instance, in a model proposed by Cremades et al in [37], an F-term from a matter-like field serves as uplifting for the cosmological constant. However, later studies by the author showed that such model fails in getting an dS/Minkowski [39]. In other words the uplifting procedure does not achieve its target.…”