Chiral Random Matrix Theories for Wilson Fermions
Savvas Zafeiropoulos, Institut für Theoretische Physik – Goethe-Universität Frankfurt
We introduce Random Matrix Models for the Wilson-Dirac operator of Quantum Chromodynamics (QCD) and QCD-like theories. We show that they are equivalent to the epsilon-limit of the chiral Lagrangian for Wilson chiral perturbation theory (WchPT), which is the low energy effective theory describing lattice QCD with Wilson fermions. Results are obtained for the Hermitian Dirac operator of two-color QCD with quarks in the fundamental representation of the color group as well as the non-Hermitian Dirac operator of SU(3) QCD. For the latter case we propose a novel way for the derivation of the Low Energy constants of WchPT. Comparisons of our analytical results with direct numerical simulations of random matrices are shown.