de Sitter vacua in no-scale supergravities and Calabi-Yau string models

TL;DR

The authors develop a Kähler-geometry–driven criterion for metastable de Sitter vacua in 4D $\mathcal{N}=1$ supergravity arising from string compactifications, showing that a positive sGoldstino mass (projected along the Goldstino direction) is necessary and, with suitable tuning of the superpotential, sufficient for overall scalar stability. They express the key stability condition through $\lambda$ and $\sigma$, with $\sigma>0$ depending only on the Kähler potential, and analyze large-volume limits (no-scale) relevant to heterotic and orientifold compactifications. In concrete classes (no-scale, factorisable, two-field) they derive when metastable vacua can exist: typically tachyonic sGoldstini arise in broad no-scale settings, while specific intersection data (e.g., discriminant $\Delta$) and subleading $\alpha'$ corrections can render $\sigma>0$ and lift instabilities, enabling dS vacua in limited cases. The results provide analytic guidance and a practical procedure for scanning string vacua, clarifying how $\,\alpha'$ corrections and compactification geometry shape the feasibility of spontaneously broken SUSY with $V\ge 0$.

Abstract

We perform a general analysis on the possibility of obtaining metastable vacua with spontaneously broken N=1 supersymmetry and non-negative cosmological constant in the moduli sector of string models. More specifically, we study the condition under which the scalar partners of the Goldstino are non-tachyonic, which depends only on the Kahler potential. This condition is not only necessary but also sufficient, in the sense that all of the other scalar fields can be given arbitrarily large positive square masses if the superpotential is suitably tuned. We consider both heterotic and orientifold string compactifications in the large-volume limit and show that the no-scale property shared by these models severely restricts the allowed values for the `sGoldstino' masses in the superpotential parameter space. We find that a positive mass term may be achieved only for certain types of compactifications and specific Goldstino directions. Additionally, we show how subleading corrections to the Kahler potential which break the no-scale property may allow to lift these masses.