Remarks on the effects of quantum corrections on moduli stabilization and de Sitter vacua in type IIB string theory

Abstract

The rôle of string loop corrections on the existence of de Sitter vacua and the moduli stabilization problem is examined in the framework of type IIB effective models. The fundamental building blocks of the proposed model are a geometric configuration with a minimum of three intersecting D7 brane stacks and an equal number of Kähler moduli, as well as a novel Einstein-Hilbert term associated with higher derivative terms of the 10-dimensional effective action. It was shown in previous works that, within this context, loop corrections appear which induce novel logarithmic volume-dependent terms in the effective potential. Furthermore, when D-term contributions (associated with the universal abelian factors of the D7 brane stacks) are considered, and certain bounds on the parameter space are imposed, all Kähler moduli are stabilized and de Sitter vacua are supported. In the present work, extending the previous analysis, a comprehensive study of the additional effects of multiple non-perturbative terms in the superpotential is undertaken. In particular, the combined effects of the logarithmic loop corrections and two non-perturbative terms with exponential dependence on different Kähler moduli have been investigated in various compactification limits. The implications of a nilpotent field are also discussed. Due to the complicated form of effective potential, various approximations are employed to probe different regions of the parameter space. In the large volume limit, a generic simple form of the potential is achieved. It is shown that a variety of fluxes exist for large as well as moderate volume compactifications which are capable of defining a de Sitter space and stabilizing the moduli fields. Finally, the so obtained effective potential appears to be promising for cosmological applications.