Flux Compactifications on Calabi-Yau Threefolds

TL;DR

This paper constructs explicit examples of flux compactifications on Calabi-Yau threefolds, demonstrating both supersymmetric and nonsupersymmetric solutions with potential implications for de Sitter vacua in string theory.

Contribution

It provides explicit solutions to flux compactifications on specific Calabi-Yau orientifolds, illustrating key ingredients for string theory de Sitter vacua constructions.

Findings

Explicit supersymmetric solutions with superpotential W

Nonsupersymmetric solutions with small W values

Illustrations of ingredients for de Sitter vacua

Abstract

The presence of RR and NS three-form fluxes in type IIB string compactification on a Calabi-Yau orientifold gives rise to a nontrivial superpotential W for the dilaton and complex structure moduli. This superpotential is computable in terms of the period integrals of the Calabi-Yau manifold. In this paper, we present explicit examples of both supersymmetric and nonsupersymmetric solutions to the resulting 4d N=1 supersymmetric no-scale supergravity, including some nonsupersymmetric solutions with relatively small values of W. Our examples arise on orientifolds of the hypersurfaces in $WP^{4}_{1,1,1,1,4}$ and $WP^{4}_{1,1,2,2,6}$. They serve as explicit illustrations of several of the ingredients which have played a role in the recent proposals for constructing de Sitter vacua of string theory.