LIGHT QUARKS, ZERO MODES, AND EXCEPTIONAL CONFIGURATIONS

In continuum QCD, nontrivial gauge topologies give rise to zero eigenv alues of the massless Dirac operator. In lattice QCD with Wilson fermi ons, analogs of these zero modes appear as exactly real eigenvalues of the Wilson-Dirac operator, leading to poles in the quark propagator i n the vicinity of the critical hopping parameter. It is shown that ''e xceptional configurations,'' which arise in the quenched approximation at small quark mass, are the result of the fluctuation of the positio n of zero mode poles to subcritical values of hopping parameter on par ticular gauge configurations. We describe a procedure for correcting t hese lattice artifacts by first isolating the contribution of zero mod e poles to the quark propagator and then shifting the subcritical pole s to the critical point. This procedure defines a modified quenched ap proximation in which accurate calculations can be carried out for arbi trarily small quark masses.