Random matrix models for the hermitian wilson-dirac operator of QCD-like theories

Abstract

We introduce Random Matrix Models for the Hermitian Wilson-Dirac operator of QCD-like theories. We show that they are equivalent to the e-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 Nc =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.