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

Understand

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.