CHIRAL HIERARCHIES, COMPOSITENESS, AND THE RENORMALIZATION-GROUP

A wide class of models involve the fine-tuning of significant hierarch ies between a strong-coupling ''compositeness'' scale and a low-energy dynamical symmetry-breaking scale. We examine the issue of whether su ch hierarchies are generally endangered by Coleman-Weinberg instabilit ies. A careful study using perturbative two-loop renormalization group methods finds that consistent large hierarchies are not generally dis allowed.