A Study of the 't Hooft Model with the Overlap Dirac Operator

TL;DR

This study explores two-dimensional QCD using overlap fermions, analyzing meson spectra, decay constants, and topological properties across different gauge groups, confirming the operator's chiral features and universality.

Contribution

It provides the first extensive numerical analysis of 2D QCD with overlap fermions across multiple gauge groups, validating theoretical relations and chiral properties.

Findings

Witten-Veneziano relation holds within errors

Chiral condensate for N_f=1 is non-zero

Results confirm universality in N_c

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 =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.