Random Matrix Models for the Hermitian Wilson-Dirac operator of QCD-like theories

TL;DR

This paper develops Random Matrix Models for the Hermitian Wilson-Dirac operator in QCD-like theories, connecting them to Wilson chiral perturbation theory and providing spectral density results with numerical validation.

Contribution

It introduces a new class of Random Matrix Models for the Hermitian Wilson-Dirac operator and links them to the epsilon-limit of Wilson chiral perturbation theory.

Findings

Established equivalence between the models and the epsilon-limit of the chiral Lagrangian.

Derived lattice spacing dependence of spectral density for two-color QCD.

Validated models through numerical simulations of the random matrix ensemble.

Abstract

We introduce Random Matrix Models for the Hermitian Wilson-Dirac operator of QCD-like theories. We show that they are equivalent to the $\epsilon$-limit of the chiral Lagrangian for Wilson chiral perturbation theory. Results are obtained for two-color QCD with quarks in the fundamental representation of the color group as well as any-color QCD with quarks in the adjoint representation. For $N_c=2$ we also have obtained the lattice spacing dependence of the quenched average spectral density for a fixed value of the index of the Dirac operator. Comparisons with direct numerical simulations of the random matrix ensemble are shown.