No metastable de Sitter vacua in N=2 supergravity with only hypermultiplets

TL;DR

The paper investigates metastable vacua in ${\cal N}=2$ supergravity with only hypermultiplets and proves a universal bound on the lightest sGoldstino mass that depends solely on the gravitino mass $m_{3/2}$ and the cosmological constant $V$, independent of quaternionic-Kähler curvature. Using the Breitenlohner-Freedman bound, it shows de Sitter vacua are excluded while AdS vacua can be metastable only if $V$ is sufficiently negative, with a rigid-limit behavior linking the bound to curvature along sGoldstino directions. The analysis parallels results for ${\cal N}=2$ theories with vector multiplets and Abelian gaugings, highlighting how restricted scalar geometries constrain metastability. The findings have implications for string-inspired model building and suggest that richer gaugings or mixed multiplet sectors may be necessary to realize metastable dS vacua in extended supergravity frameworks.

Abstract

We study the stability of vacua with spontaneously broken supersymmetry in N=2 supergravity theories with only hypermultiplets. Focusing on the projection of the scalar mass matrix along the sGoldstino directions, we are able to derive a universal upper bound on the lowest mass eigenvalue. This bound only depends on the gravitino mass and the cosmological constant, but not on the details of the quaternionic manifold spanned by the scalar fields. Comparing with the Breitenlohner-Freedman bound shows that metastability requires the cosmological constant to be smaller than a certain negative critical value. Therefore, only AdS vacua with a sufficiently negative cosmological constant can be stable, while Minkowski and dS vacua necessarily have a tachyonic direction.