On the distribution of stable de Sitter vacua

TL;DR

This paper explores the rarity of stable de Sitter vacua in string theory, demonstrating that such solutions are scarce and tend to cluster at small cosmological constants, especially when non-geometric fluxes are considered.

Contribution

It introduces a systematic method for analyzing stable de Sitter solutions in type II string theory with non-geometric fluxes, highlighting their scarcity and specific distribution in parameter space.

Findings

Stable de Sitter vacua are rare in string theory.

Non-geometric fluxes are essential for stability.

Stable solutions cluster at small cosmological constants.

Abstract

The possible existence of (meta-) stable de Sitter vacua in string theory is of fundamental importance. So far, there are no fully stable solutions where all effects are under perturbative control. In this paper we investigate the presence of stable de Sitter vacua in type II string theory with non-geometric fluxes. We introduce a systematic method for solving the equations of motion at the origin of moduli space, by expressing the fluxes in terms of the supersymmetry breaking parameters. As a particular example, we revisit the geometric type IIA compactifications, and argue that non-geometric fluxes are necessary to have (isotropically) stable de Sitter solutions. We also analyse a class of type II compactifications with non-geometric fluxes, and study the distribution of (isotropically) stable de Sitter points in the parameter space. We do this through a random scan as well as through a complementary analysis of two-dimensional slices of the parameter space. We find that the (isotropically) stable de Sitter vacua are surprisingly rare, and organise themselves into thin sheets at small values of the cosmological constant.