Gauge invariance of fermion masses in extended-technicolor theories

It has recently been argued that, in technicolor theories, large quark and lepton masses can arise if the extended-technicolor (ETC) interactions play an important direct role in chiral-symmetry breaking. This happens when the ETC coupling is sufficiently close to a critical value. The analysis that led to these conclusions was based on the study of the renormalization-group-improved ladder Dyson-Schwinger equation. In this paper we investigate the gauge invariance of this ETC-driven fermion-mass enhancement. We show that the critical curve in the ETC, technicolor coupling plane, separating the symmetric and symmetry-breaking phases, is gauge invariant. We then show that the same is true for fermion-mass enhancement