No-scale supergravity

To connect supergravity with the real world, a highly non-trivial requirement is complete spontaneous supersymmetry breaking in an approximately flat four-dimensional space-time. In no-scale supergravity models, this naturally happens at the classical level: the gravitino mass, setting the scale of supersymmetry breaking, slides along a flat direction of the potential with vanishing energy. This contribution briefly describes, with a personal selection of simple illustrative examples, some qualitative features of no-scale models that relate them to a possible dynamical generation of the hierarchies between the vacuum energy scale, the weak scale and the Planck scale. It includes comments on their versions with extended supersymmetry, on their higher-dimensional origin and on how their still unsolved problems of quantum stability can already be addressed, with some results, at the level of supergravity compactifications, although their solution (if any) will eventually require a better understanding of superstring theories.