Inverted sparticle hierarchies from natural particle hierarchies

A possible resolution of the flavor puzzle is that the fermion mass hierarchy can be dynamically generated through the coupling of the first-two-generation fields to a strongly coupled sector, which is approximately conformally invariant and leads to large anomalous dimensions for the first-two-generation fields over a large range of energies. We investigate the possibility of using the same sector to also break supersymmetry. We show that this automatically gives an "inverted hierarchy'' in which the first-two-generation squarks and sleptons are much heavier than the other superpartners. Implementing this construction generically requires some fine-tuning in order to satisfy the constraints on flavor-changing neutral currents at the same time as solving the hierarchy problem. We show that this fine-tuning can be reduced to be milder than the percent level by making some technically natural assumptions about the form of the strongly coupled sector and its couplings to the standard model.