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 $\mathrm{SU}\mathrm{}\left(N\right)\mathrm{}\times \mathrm{SU}\mathrm{}\left(N\right)\mathrm{}$ chiral symmetry of a model with $N$ species of massless fermions is spontaneously broken by this effect, and $N^2-1\mathrm{}$ 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.