Weak scale supersymmetry without weak scale supergravity

It is generally believed that weak scale supersymmetry implies weak scale supergravity, in the sense that the masses of the gravitino and gravitationally coupled moduli have masses below 100 TeV. This Letter presents a realistic framework for supersymmetry breaking in which these masses can be much larger. This solves the cosmological problems of hidden sector models. Supersymmetry breaking is communicated to the visible sector by anomaly-mediated supersymmetry breaking. The framework is compatible with perturbative gauge coupling unification and can be realized either in models of 'warped' extra dimensions or in strongly coupled four-dimensional conformal field theories