De Sitter hunting in a classical landscape

TL;DR

This paper systematically explores the construction of de Sitter solutions in type IIA string theory on SU(3)-structure manifolds, highlighting new solutions and the challenges in achieving fully consistent, stable vacua.

Contribution

It classifies geometries suitable for de Sitter solutions and performs a systematic scan for such solutions, emphasizing the difficulties in constructing explicit, stable, and localized vacua.

Findings

Many new de Sitter solutions found as critical points of the 4D potential.

Identified key challenges such as stability, charge quantization, and localization.

Provided a pedagogical guide for constructing and analyzing these solutions.

Abstract

We elaborate on the construction of de Sitter solutions from IIA orientifolds of SU(3)-structure manifolds that solve the 10-dimensional equations of motion at tree-level in the approximation of smeared sources. First we classify geometries that are orbifolds of a group manifold covering space which, upon the proper inclusion of O6 planes, can be described within the framework of N=1 supergravity in 4D. Then we scan systematically for de Sitter solutions, obtained as critical points of an effective 4D potential. Apart from finding many new solutions we emphasize the challenges in constructing explicit classical de Sitter vacua, which have sofar not been met. These challenges are interesting avenues for further research and include finding solutions that are perturbatively stable, satisfy charge and flux quantization, and have genuine localized (versus smeared) orientifold sources. This paper intends to be self-contained and pedagogical, and thus can serve as a guide to the necessary technical tools required for this line of research. In an appendix we explain how to study flux and charge quantization in the presence of a non-trivial H-field using twisted homology.