Towards Classical de Sitter Solutions in String Theory

TL;DR

This paper explores the conditions for realizing classical de Sitter solutions in string theory, analyzing flux compactifications and torsion classes, and finds new non-supersymmetric AdS solutions but no explicit de Sitter solutions.

Contribution

It derives explicit criteria for de Sitter solutions in type II string compactifications and tests these on specific manifolds, identifying limitations and new AdS solutions.

Findings

De Sitter solutions cannot be realized on the examined manifolds.

New non-supersymmetric AdS solutions are found for certain cosets.

Explicit torsion conditions are derived for de Sitter solutions.

Abstract

We investigate the type II string effective potential at tree-level and derive necessary ingredients for having de Sitter solutions in orientifold models with fluxes. Furthermore, we examine some explicit O6 compactifications in IIA supergravity on manifolds with SU(3)-structure in the limit where the orientifold sources are smeared. In particular, we use a simple ten-dimensional Ansatz for four-dimensional de Sitter solutions and find the explicit criteria in terms of the torsion classes such that these de Sitter solutions solve the equations of motion. We have verified these torsion conditions for the cosets and the Iwasawa manifold and it turns out that the conditions cannot be fulfilled for these spaces. However, this investigation allows us to find new non-supersymmetric AdS solutions for some cosets. It remains an open question whether there exist SU(3)-structure manifolds that satisfy the conditions on the torsion classes for these simple de Sitter solutions to exist.