Complementarity - the absence of a phase boundary separating the Higgs and confinement phases of a gauge theory - can be violated by the addition of chiral fermions. We utilize chiral symmetry violating fermion correlators such as ⟨\bpsψ⟩ as order parameters to investigate this issue. Using inequalities similar to those of Vafa-Witten and Weingarten, we show that SU(2) gauge theories with Higgs and fermion fields in the fundamental representation exhibit chiral symmetry breaking in the confined phase and therefore do {\it not} lead to massless composite fermions. We discuss the implications for the Abbott-Farhi strongly interacting standard model.
@article{arxiv.hep-ph/9302235,
title = {Complementarity and Chiral Fermions in SU(2) gauge Theories},
author = {Stephen D. H. Hsu},
journal= {arXiv preprint arXiv:hep-ph/9302235},
year = {2009}
}