General analysis of moduli stabilization in type IIB string compactifications

In the context of type IIB superstring flux-compactifications on Calabi Yau orientifolds, stabilizing the Kähler moduli is crucially challenging due to the tree-level protection arising from the so-called "No-scale structure". The breaking of this no-scale effective symmetry is paramount within the process of moduli stabilization; this work is aimed at studying the ways of a controlled breaking of this effective symmetry using some sub-leading effects such as perturbative α′-corrections to the Kähler potential and non-perturbative effects to the superpotential. The same have led to three attractive and well-established schemes for moduli stabilization, namely the KKLT scheme, the racetrack scheme and the Large Volume Scenarios (LVS) scheme. The main goal for the present work is twofold; first to study the scalar potential for closed-string moduli in a quite model-independent way which will subsequently enable to understand some interesting features of the no-scale structure breaking, second, to provide a unified framework for the above mentioned three well-known schemes for moduli stabilization. Our generic approach not only helps in directly reading-off the scalar potentials of these schemes via merely knowing some topo- logical data (such as intersection numbers) of the compactifying Calabi Yau, but being generic it also provides the hope both for some useful extensions of these schemes and for the possibility of finding a new moduli stabilization scheme, e.g. using odd moduli. Moreover, this approach might ultimately lead to performing a model independent analysis for moduli stabilization, for example via creating the possibility of finding some general conditions for the existence of stable de-Sitter vacua for arbitrary compactifcations, as would be highly desirable.