32nd International Symposium on Lattice Field Theory (Lattice 2014)

The Chiral Condensate of One-Flavor QCD and the Dirac Spectrum at θ=0

25 Jun 2014, 09:00

20m

309 Havemeyer

Talk Chiral Symmetry Chiral Symmetry

Speaker

Prof. Jacobus Verbaarschot (Stony Brook University)

Description

In a sector of fixed topological charge, the chiral condensate has a discontinuty given by the Banks-Casher formula also in the case of one-flavor QCD. However, at fixed $\theta$ angle, the chiral condensate remains constant when the quark mass crosses zero. To reconcile these contradictory observations, we have evaluated the spectral density of one-flavor QCD at $\theta =0$. For negative quark mass, it becomes a strongly oscillating function with a period given by the inverse space-time volume and an amplitude that increases expoentially with the space-time volume. As we have learned from QCD at nonzero chemical potential, if this is the case, an alternative to the Banks-Casher formula applies, and we will demonstrate that for one-flavor QCD, this results into a continuous chiral condensate. A special role is played by the topological zero modes which have to be taken into account exactly in order to get a finite chiral condensate in the thermodynamic limit.

Presentation materials

Slides

lat-14-verbaarschot.pdf