"One-Flavor QCD and the Dirac Spectrum at $\theta=0$"

Presented by Jacobus Verbaarschot, Stony Brook University

Thursday, June 25, 2015, 12:30 pm — Building 510 Room 2-160

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.