Study of the ’t Hooft model with the overlap Dirac operator

Abstract

We present the results of an exploratory numerical study of two dimensional QCD with overlap fermions. We have performed extensive simulations for ${U(N}_{c})$ and ${SU(N}_{c})$ color groups with ${N}_{c}=2,3,4$ and coupling constants chosen to satisfy the 't Hooft condition ${g}^{2}{N}_{c}=\mathrm{const}=4/3.$ We have computed the meson spectrum and decay constants, the topological susceptibility and the chiral condensate. For ${U(N}_{c})$ gauge groups, our results indicate that the Witten-Veneziano relation is satisfied within our statistical errors and that the chiral condensate for ${N}_{f}=1$ is compatible with a non-zero value. Our results exhibit universality in ${N}_{c}$ and confirm once more the excellent chiral properties of the overlap-Dirac operator.