Minimal low energy supergravity

I discuss some aspects of minimal low energy N=1 supergravity models related with gauge symmetry breaking and the naturalness criterion. I show: i) how a small μ-term can naturally arise, explaining the Fermi scale only in terms of supergravity breaking; ii) how the naturalness criterion provides upper bounds for all supersymmetric particle masses; iii) how the experimental search for supersymmetry at future colliders can be best compared with theory in the plane of the relevant supersymmetric parameters and how this plane is constrained by SU(2) x U(1) breaking