Abstract:Année de publication : 2011
This thesis is devoted to the study of non–supersymmetric flux compactifications in type IIA string theory. After a brief review of type II theories, we introduce the mathematical framework of Generalized Complex Geometry, which provides an encompassing geometric interpretation and organizing principle for supersymmetric vacua. We introduce the class of solvmanifolds, which have been extensively used as compactification manifolds, and discuss their mathematical properties, with particular attention to the compactness criteria. We then present our first example of non-supersymmetric compactification, a vacuum which has a de Sitter external space. We solve the equations of motion and in the process we argue about the behavior of D–branes in non–supersymmetric backgrounds; a short analysis of the four dimensional physics is also provided. We speculate about the use of Generalized Geometry for non-supersymmetric vacua too and about the right variables to describe the supposed underlying geometric structure. Motivated by AdS/CFT considerations we investigate a supersymmetry breaking vacuum which is supposed to be the gravity dual to a metastable non–supersymmetric vacuum of a supersymmetric gauge theory. Supersymmetry is here broken by the addition of anti–branes; it is notoriously difficult to take into account their backreaction and we resort to use a perturbative technique. We compute the most general first order deformations of a D2–brane background, discuss the space of solutions of the deformed fields and argue about the nature of the unavoidable singularities which we encounter in the process.