Singular points in compactifications of type IIA string theory

Abstract

In this thesis, singular loci in Kähler moduli space of type IIA string theory on a Calabi-Yau threefold are considered. The compactification of type IIA string theory to 4D is described and the moduli spaces of the Calabi-Yau threefold are introduced. Then, singularities in the Kähler moduli space are discussed and classified using the theory of mixed Hodge structures and nilpotent orbits, which is introduced in some detail. We use this classification of singular loci to find constraints on the triple intersection numbers that occur in the metric of type IIA Kähler moduli space. These are classified in terms of the various singularity types. We also try to find `ficticious' intersection numbers that violate the constraints, finding that these usually seem to yield moduli space metrics that degenerate somewhere on moduli space. This leads one to propose that this feature might be true in general. Lastly, we also describe the nilpotent orbits arising near the singular loci from a slightly different viewpoint, in which their nilpotent generators relate flux configurations of different kinds and are interpreted in terms of Freed-Witten anomalous branes attached to domain walls in the 4D theory.