Abstract:Année de publication : 2013
The subject of this thesis is the study of non-supersymmetric solutions of string theory. Their use is of fundamental importance in a variety of applications: in gauge/gravity correspondence, to construct gravity duals to non-supersymmetric vacua and models of mediated supersymmetry breaking; in cosmology, to construct de Sitter vacua and to study the cosmological constant problem; for black holes, to construct their microstates. More broadly, it is important to study the solution space of string theory and to understand its deep mathematical structures beyond the simplifications which stem from supersymmetry. We mainly consider solutions in the supergravity limit. We construct a vast space of non-supersymmetric perturbations around supergravity solutions dual to confining supersymmetric gauge theories, in four and three dimensions. We then proceed to a rigorous and detailed study of a particular way to break supersymmetry in flux compactifications, namely by adding some branes with charge of opposite sign with respect to the fluxes. We discover that the supergravity solution corresponding to these objects is singular, and we discuss in details possible string theory resolutions of this singularity. We then consider the consequences of these results both for the existence of metastable non-supersymmetric states in the dual field theories and for the existence of a large landscape of de Sitter vacua in string theory.