On classical de Sitter solutions in higher dimensions

TL;DR

This paper establishes necessary conditions for classical de Sitter solutions in higher-dimensional flux compactifications, revealing strict limitations and the necessity of negative curvature in the compact dimensions.

Contribution

It provides the first set of necessary criteria for classical de Sitter solutions in higher dimensions and identifies specific models that satisfy these conditions.

Findings

De Sitter solutions are highly restricted in higher dimensions.

Only certain O6 and O5 compactifications satisfy the criteria.

No meta-stable solutions exist above six dimensions.

Abstract

We derive necessary criteria for the existence of classical, meta-stable, de Sitter solutions in flux compactifications of type II supergravity down to dimensions higher than four. We find that the possibilities in higher dimensions are much more restricted than in four dimensions. The only models that satisfy the criteria are derived from O6 compactifications to D=5,6 and O5 compactifications to D=5 and no meta-stable solutions can exist in dimensions higher than six. All these models have in common that the compact dimensions are negatively curved.