Interaction of massless fermions with instantons

Abstract

We develop a systematic method of calculating the massless fermion propagation function and fermion-induced effective action in the background gauge field of an arbitrary number of widely separated instantons and anti-instantons. The results exhibit a strongly non-local nature of instanton interactions with massless fermions. Using these results, we also demonstrate that the ordinary perturbation theory vacuum is not allowed in QCD with massless fermions, since the cluster decomposition for certain correlation functions is violated due to widely separated instanton-anti-instanton bound states. The underlying mechanism is identical to that in the Schwinger model.