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

TL;DR

This paper proves that in N=2 supergravity with only hypermultiplets, stable de Sitter vacua cannot exist, and only certain anti-de Sitter vacua are stable due to universal bounds on scalar masses.

Contribution

It establishes a universal upper bound on scalar masses in N=2 supergravity with hypermultiplets, showing the non-existence of metastable de Sitter vacua.

Findings

Stable vacua require a sufficiently negative cosmological constant.

Minkowski and de Sitter vacua necessarily have tachyonic directions.

Only anti-de Sitter vacua with large negative cosmological constant can be stable.

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.