Bound states from instantons

Abstract

The pseudoparticle solutions of non-Abelian gauge theories can generate a mass for fermions coupled to the gauge fields. The $\mathrm{SU}(N)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(N)$ chiral symmetry of a model with $N$ species of massless fermions is spontaneously broken by this effect, and ${N}^{2}\ensuremath{-}1$ Goldstone bosons are consequently formed as bound states of fermion-antifermion pairs. We demonstrate these facts explicitly in models with one or two species of fermions. The mechanism by which the fermions acquire a mass is such that the symmetries $P$ and $T$ are conserved even in the presence of pseudoparticles.