Low-lying fermion modes, topology, and light hadrons in quenched QCD

We explore the properties of low lying eigenmodes of fermions in the quenched approximation of lattice QCD. The fermion action is a recently proposed overlap action and has exact chiral symmetry. We find that chiral zero-eigenvalue modes are localized in space and their positions correlate strongly with the locations (as defined through the density of pure gauge observables) of instantons of the appropriate charge. Nonchiral modes are also localized with peaks that are strongly correlated with the positions of both charges of instantons. These correlations slowly die away as the fermion eigenvalue rises. Correlators made of quark propagators restricted to these modes closely reproduce ordinary hadron correlators at small quark mass in many channels. Our results are in qualitative agreement with the expectations of instanton liquid models.