A Universal Tachyon in Nearly No-scale de Sitter Compactifications

TL;DR

The work shows that near any no-scale Minkowski point, a large class of 4d N=1 F-term supergravity models inevitably harbor a tachyon with η ≤ -4/3, ruling out meta-stable de Sitter vacua and slow-roll inflation in these regimes. The tachyon is universal but its exact field-space direction depends on model details, aligning with the sgoldstino in the Minkowski limit and moving away from it when deforming away from the Minkowski point. Stability of the sgoldstino can persist due to mass mixing, implying that metastability is not universally prohibited for all directions. Evading the no-go generally requires substantial perturbative Kähler corrections, nonzero W_{amn} couplings, or at least one unstabilized Φ^a, and often relies on ingredients beyond classical geometric fluxes, such as instantons or non-geometric fluxes, consistent with existing constructions that achieve meta-stable dS vacua.

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 $η\le -\frac{4}{3}$ 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 Kähler 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.