New models of gauge- and gravity-mediated supersymmetry breaking

We show that supersymmetry breaking in a class of theories with SU$\mathrm{}\left(N\right)\mathrm{}\times \mathrm{SU}\left(N-2\right)$ gauge symmetry can be studied in a calculable $\sigma$ model. We use the $\sigma$ model to show that the supersymmetry-breaking vacuum in these theories leaves a large subgroup of flavor symmetries intact, and to calculate the masses of the low-lying states. By embedding the standard model gauge groups in the unbroken flavor symmetry group we construct a class of models in which supersymmetry breaking is communicated by both gravitational and gauge interactions. One distinguishing feature of these models is that the messenger fields, responsible for the gauge-mediated communication of supersymmetry breaking, are an integral part of the supersymmetry-breaking sector. We also show how, by lowering the scale that suppresses the nonrenormalizable operators, a class of purely gauge-mediated models with a combined supersymmetry-breaking-cum-messenger sector can be built. We briefly discuss the phenomenological features of the models we construct.