Scalar masses in general N=2 gauged supergravity theories

TL;DR

This paper investigates the existence of universal upper bounds on scalar masses in N=2 gauged supergravity, revealing conditions under which metastable de Sitter vacua can occur based on the number of gauged isometries.

Contribution

It extends previous bounds to theories with hyper and vector multiplets and clarifies the role of the number of gauged generators in the existence of bounds.

Findings

Bounds exist for theories with a single gauged isometry for both positive and negative cosmological constant.

No universal bound exists when two or more isometries are gauged.

Metastable de Sitter vacua with small V can only occur with at least two gauged isometries.

Abstract

We readdress the question of whether any universal upper bound exists on the square mass m^2 of the lightest scalar around a supersymmetry breaking vacuum in generic N=2 gauged supergravity theories for a given gravitino mass m_3/2 and cosmological constant V. We review the known bounds which apply to theories with restricted matter content from a new perspective. We then extend these results to theories with both hyper and vector multiplets and a gauging involving only one generator, for which we show that such a bound exists for both V>0 and V<0. We finally argue that there is no bound for the same theories with a gauging involving two or more generators. These results imply that in N=2 supergravity theories metastable de Sitter vacua with V<<m^2_3/2 can only arise if at least two isometries are gauged, while those with V>>m^2_3/2 can also arise when a single isometry is gauged.