Dirac Spectrum of the Wilson Dirac Operator for QCD with Two Colors

TL;DR

This paper analyzes the spectral properties of the Wilson Dirac operator in two-color QCD using chiral perturbation theory, providing analytical results and confirming them with Monte Carlo simulations to understand lattice artefacts.

Contribution

It offers new analytical expressions for spectral observables of the Wilson Dirac operator in two-color QCD and links these to lattice artefacts through random matrix theory validation.

Findings

Derived analytical formulas for level density and chirality distribution.

Established constraints for real eigenvalues and real modes.

Confirmed results with Monte Carlo simulations.

Abstract

We study the lattice artefacts of the Wilson Dirac operator for QCD with two colors and fermions in the fundamental representation from the viewpoint of chiral perturbation theory. These effects are studied with the help of the following spectral observables: the level density of the Hermitian Wilson Dirac operator, the distribution of chirality over the real eigenvalues, and the chiral condensate for the quenched as well as for the unquenched theory. We provide analytical expressions for all these quantities. Moreover we derive constraints for the level density of the real eigenvalues of the non-Hermitian Wilson Dirac operator and the number of additional real modes. The latter is a good measure for the strength of lattice artefacts. All computations are confirmed by Monte Carlo simulations of the corresponding random matrix theory which agrees with chiral perturbation theory of two color QCD with Wilson fermions.