Light quarks, zero modes, and exceptional configurations

In continuum QCD, nontrivial gauge topologies give rise to zero eigenvalues of the massless Dirac operator. In lattice QCD with Wilson fermions, analogs of these zero modes appear as exactly real eigenvalues of the Wilson-Dirac operator, leading to poles in the quark propagator in the vicinity of the critical hopping parameter. It is shown that "exceptional configurations," which arise in the quenched approximation at small quark mass, are the result of the fluctuation of the position of zero mode poles to subcritical values of hopping parameter on particular gauge configurations. We describe a procedure for correcting these lattice artifacts by first isolating the contribution of zero mode poles to the quark propagator and then shifting the subcritical poles to the critical point. This procedure defines a modified quenched approximation in which accurate calculations can be carried out for arbitrarily small quark masses.