Abstract
Critical dynamics constrains models of dynamical electroweak symmetry breaking in which the scale of high-energy physics is far above 1 TeV. A big hierarchy requires the high-energy theory to have a second-order chiral phase transition, near which the theory is described by a low-energy effective Lagrangian with composite ``Higgs'' scalars. As scalar theories with more than one ${\mathrm{\ensuremath{\Phi}}}^{4}$ coupling can have a Coleman-Weinberg instability and a first-order transition, such dynamical EWSB models cannot always support a large hierarchy. If the large-${\mathit{N}}_{\mathit{c}}$ Nambu--Jona-Lasinio model is a good approximation to the top-condensate and strong extended technicolor models, they will not produce acceptable EWSB.
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