Distribution of the Dirac modes in QCD
The equivalence between the partition function of QCD in the lowest energy limit and the partition function predicted by the Chiral Random Matrix Theory is well established through the use of the Chiral Perturbation Theory. In particular the ChRMT provides a description of the low-lying eigenvalues of the euclidean Dirac operator. In this work we study, on the lattice, the spectrum of the overlap Dirac operator out of the ε-regime. We find that not only the lowest eigenvalues are well-described by the ChRMT but also the higher eigenvalue distribution can also be explained through the Random Matrix Theory using the Gaussian Unitary Ensemble. However, these higher eigenvalues are not related to the chiral symmetry breaking and connected to the confinement physics. They are consistent with the observed earlier SU(4) symmetry.