Flux Vacua and the Web of Type II Compactifications

Abstract

This dissertation investigates the period geometry in compactifications of type IIB string theory on restricted moduli spaces in the context of supersymmetric flux vacua and black hole condensations. The guiding question of this work is how transitions among families of Calabi–Yau manifolds connect the vast number of seemingly different compactifications. We show that fixed-point loci in the complex-structure moduli space under suitable discrete symmetries furnish a rational splitting of periods, which is necessary for symmetric moduli stabilisation and embeds known flux vacua into multi-parameter models. We reduce the search for flux vacua in compactifications on one-parameter Calabi–Yau four-folds to attractor points on their Yifan-Yang pullback. Along singular components of the moduli space, we identify one-parameter models arising in strong coupling and conifold transitions. In the latter case, black hole condensation smooths out the singularity and gives rise to a mixed Coulomb/Higgs branch with an induced integral period structure. We categorise the transitions in genus-one fibrations over toric bases described by reflexive polygons and identify new connections among several families. A formalism is proposed that constructs conjecturally integral period bases for (<em>n</em> > 3)-dimensional non-degenerate Calabi–Yau families, which is supported by exemplary computations.