A non-perturbative mechanism for fermion mass generation

In this talk I present (numerical) evidence for the existence of a field-theoretical mechanism that can provide mass to fermions in models with fermions, non-abelian gauge fields and scalars, where chiral symmetry is broken at the cutoff level by some irrelevant term, provided the model parameters are tuned to critical values at which chiral symmetry is maximally restored. We show that in the Nambu-Goldstone phase of the critical model fermions acquire a non-perturbative mass of the order of the RGI scale of the theory times powers of the coupling constant of the gauge interaction the fermion is subjected to and independent of the scalar vev. The peculiar structure of this mass term 1) suggests the existence of a super-strong non-abelian sector at the (multi)TeV scale as, in order to have the top mass at its physical value, the RGI scale of the theory must be much larger than $\Lambda_{QCD}$, 2) it suggests that the fermion mass hierarchy is a consequence of the different strength of the interaction the particles feel.

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