Massless composite fermions and discrete chiral symmetries

Abstract

Massless composite quarks and leptons require unbroken chiral symmetries. The 't Hooft anomaly conditions usually prevent the construction of realistic models with such symmetries. We consider a class of models in which the original chiral symmetry is broken, leaving a conserved discrete chiral group, allowing for massless composite fermions but evading the 't Hooft condition. Several explicit examples are considered. In all cases, the massless fermions are accompanied by Goldstone bosons which, however, decouple from all low-energy phenomena.