Topology and the Dirac Spectrum for One-Flavor QCD

Abstract

The chiral condensate of one-flavor QCD is continuous when the quark mass|crosses zero. In the sector of fixed topological charge though, the chiral condensate becomes discontinuous at zero mass in the the thermodynamical|limit. To reconcile these contradictory observations, we have evaluated|the spectral density of the Dirac operator in the epsilon domain of |one-flavor QCD. In this domain, we have obtained exact analytical expressions which show that the spectral density at $\theta = 0$ becomes a |strongly oscillating function for negative quark mass with an amplitude|that increases exponentially with the volume. As is the case for QCD at|nonzero chemical potential, these strong oscillations invalidate the|Banks-Casher formula and result in a chiral condensate that is continuous|as a function of the quark mass. An additional subtlety is the effect|of the topological zero modes which will be discussed as well.