Constraints on Meta-stable de Sitter Flux Vacua

TL;DR

This paper demonstrates that under certain conditions in type IIB flux compactifications, meta-stable de Sitter vacua cannot exist due to inherent tachyonic instabilities, impacting the landscape of string theory vacua.

Contribution

It provides a general proof that meta-stable de Sitter vacua are impossible in a specific flux compactification limit, independent of Calabi-Yau geometry details.

Findings

No meta-stable de Sitter vacua in the considered limit.

Stability relates cosmological constant to supersymmetry breaking scale.

Constraints influence the statistical distribution of vacua.

Abstract

We consider flux compactification of type IIB string theory as the orientifold limit of an F-theory on a Calabi-Yau fourfold. We show that when supersymmetry is dominantly broken by the axion-dilaton and the contributions of the F-terms associated with complex structure moduli are small, the Hessian of the flux potential always has tachyonic modes for de Sitter vacua. This implies that there exist no meta-stable de Sitter vacua in this limit. Moreover, we find that the stability requirement imposes a relation between the values of cosmological constant and the scale of supersymmetry breaking for non-supersymmetric anti de Sitter vacua in this limit. The proof is general and does not rely on the details of the geometry of the compact Calabi-Yau internal space. We finally analyze the consequences of these constraints on the statistics of meta-stable de Sitter vacua and address some other related issues.