F-Theory and the Landscape of Intersecting D7-Branes

Abstract

In this work, the moduli of D7-branes in type IIB orientifold compactifications and their stabilization by fluxes is studied from the perspective of F-theory. In F-theory, the moduli of the D7-branes and the moduli of the orientifold are unified in the moduli space of an elliptic Calabi-Yau manifold. This makes it possible to study the flux stabilization of D7-branes in an elegant manner. To answer phenomenological questions, one has to translate the deformations of the elliptic Calabi-Yau manifold of F-theory back to the positions and the shape of the D7-branes. We address this problem by constructing the homology cycles that are relevant for the deformations of the elliptic Calabi-Yau manifold. We show the viability of our approach for the case of elliptic two- and three-folds. Furthermore, we discuss consistency conditions related to the intersections between D7-branes and orientifold planes which are automatically fulfilled in F-theory. Finally, we use our results to study the flux stabilization of D7-branes on the orientifold $K3\times T^2/\Z_2$ using F-theory on $K3\times K3$. In this context, we derive conditions on the fluxes to stabilize a given configuration of D7-branes. This thesis furthermore contains an introduction to F-theory and a brief review of some mathematical background.