The spectrum of D-slash in QCD via replicas

Abstract

This is a short review of the derivation of the spectrum of the Dirac operator in QCD4 in a finite volume V by means of the replica trick. The derivation is nonperturbative in the QCD coupling and it is in agreement with lattice results as well as chiral random matrix theory (ChRMT). Our results hold in the energy scale where chiral symmetry is broken and the Pion wavelength is much bigger than the size of the system (pi >>> V ¼).