A Universal Tachyon in Nearly No-scale de Sitter Compactifications

TL;DR

This paper demonstrates that a broad class of de Sitter solutions in supergravity models near no-scale Minkowski points inherently contain a universal tachyon, preventing stable de Sitter vacua and slow-roll inflation.

Contribution

It reveals a universal tachyonic instability in nearly no-scale de Sitter compactifications, providing conditions to avoid it and explaining challenges in classical de Sitter construction.

Findings

Most solutions have a tachyon with η ≤ -4/3 at positive vacuum energy.

The tachyon aligns with the sgoldstino in the Minkowski limit.

Superpotential and Kähler potential conditions can prevent the instability.

Abstract

We investigate de Sitter solutions of $\mathcal{N}=1$ supergravity with an F-term scalar potential near a no-scale Minkowski point, as they may in particular arise from flux compactifications in string theory. We show that a large class of such solutions has a universal tachyon with $\eta \le -\frac{4}{3}$ at positive vacuum energies, thus forbidding meta-stable de Sitter vacua and slow-roll inflation. The tachyon aligns with the sgoldstino in the Minkowski limit, whereas the sgoldstino itself is generically stable in the de Sitter vacuum due to mass mixing effects. We specify necessary conditions for the superpotential and the K\"{a}hler potential to avoid the instability. Our result may also help to explain why the program of classical de Sitter hunting has remained unsuccessful, while constructions involving instantons or non-geometric fluxes have led to various examples of meta-stable de Sitter vacua.