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

Understand

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.