F-Theory and the Landscape of Intersecting D7-Branes

TL;DR

This paper explores how F-theory provides a unified framework to study D7-brane moduli stabilization via fluxes in type IIB compactifications, with explicit constructions and stability conditions.

Contribution

It introduces a method to translate elliptic Calabi-Yau deformations into D7-brane configurations and analyzes flux stabilization conditions in specific compactifications.

Findings

Constructed homology cycles for elliptic Calabi-Yau deformations.

Demonstrated flux stabilization conditions for D7-branes.

Showed automatic fulfillment of intersection consistency conditions in F-theory.

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.