Simple de Sitter Solutions

TL;DR

This paper develops a framework for constructing metastable de Sitter solutions in type IIA string theory, demonstrating how to achieve small Hubble scales and controlled moduli stabilization using Nil manifold compactifications with fluxes and orientifolds.

Contribution

It introduces a new method for building metastable de Sitter vacua in type IIA string theory with tunable scales and controlled moduli, utilizing Nil manifold compactifications and fluxes.

Findings

Metastable de Sitter minima found in Nil manifold compactifications.

Parametric control over curvature, fluxes, and string coupling achieved.

Method to separate moduli and KK/winding scales demonstrated.

Abstract

We present a framework for de Sitter model building in type IIA string theory, illustrated with specific examples. We find metastable dS minima of the potential for moduli obtained from a compactification on a product of two Nil three-manifolds (which have negative scalar curvature) combined with orientifolds, branes, fractional Chern-Simons forms, and fluxes. As a discrete quantum number is taken large, the curvature, field strengths, inverse volume, and four dimensional string coupling become parametrically small, and the de Sitter Hubble scale can be tuned parametrically smaller than the scales of the moduli, KK, and winding mode masses. A subtle point in the construction is that although the curvature remains consistently weak, the circle fibers of the nilmanifolds become very small in this limit (though this is avoided in illustrative solutions at modest values of the parameters). In the simplest version of the construction, the heaviest moduli masses are parametrically of the same order as the lightest KK and winding masses. However, we provide a method for separating these marginally overlapping scales, and more generally the underlying supersymmetry of the model protects against large corrections to the low-energy moduli potential.