Scalar masses in general N=2 gauged supergravity theories

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We readdress the question of whether any universal upper bound exists on the square mass m² of the lightest scalar around a supersymmetry breaking vacuum in generic N=2 gauged supergravity theories for a given gravitino mass m₃/2 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<<m²₃/2 can only arise if at least two isometries are gauged, while those with V>>m²₃/2 can also arise when a single isometry is gauged.