Chiral symmetry breaking and instantons in both quenched and full QCD

Abstract

We investigate the contribution that instantons make to the QCD chiral condensate for Nf= 0, 1 and 2 quark flavours. We use a simplified model: the instantons are a (weighted) gas, the fermionic integrations are restricted to the subspace spanned by the would-be zero-modes and only the dimensional and chiral features of the Dirac operator are retained. Previous work along these lines found a power-like divergence of the Dirac spectral density at zero eigenvalue. By changing the various components of the model, we show that a power divergence appears to be a generic feature of instanton mixing for both Nf=0 and Nf=/=0. In the latter case the divergence disappears as m->0 in such a way that psibar-psi remains finite. We find that the exponent of the power decreases for larger instanton densities, becoming negligible for very dense instanton `gases'. We reproduce the expected m-dependence of the topological susceptibility, we investigate the space-time structure of the eigenfunctions, as a function of the eigenvalue, and we calculate the eta-prime mass. In summary: instantons appear to provide a natural mechanism for the spontaneous breaking of chiral symmetry in QCD, but they typically produce a power-like divergence in the Dirac spectral density. This divergence is non-standard but `harmless' in the case of full QCD, and implies a pathology in the case of quenched QCD.