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We study the scalar mass matrix of general supersymmetric theories with localgauge symmetries, and derive an absolute upper bound on the lightest scalarmass. This bound can be saturated by suitably tuning the superpotential, andits positivity therefore represents a necessary and sufficient condition forthe existence of metastable vacua. It is derived by looking at the subspace ofall those directions in field space for which an arbitrary supersymmetric massterm is not allowed and scalar masses are controlled by supersymmetry-breakingsplitting effects. This subspace includes not only the direction ofsupersymmetry breaking, but also the directions of gauge symmetry breaking andthe lightest scalar is in general a linear combination of fields spanning allthese directions. We present explicit results for the simplest case of theorieswith a single local gauge symmetry. For renormalizable gauge theories, thelightest scalar is a combination of the Goldstino partners and its square massis always positive. For more general non-linear sigma models, on the otherhand, the lightest scalar can involve also the Goldstone partner and its squaremass is not always positive.

The lightest scalar in theories with broken supersymmetry