Distribution of the Dirac modes in QCD

Abstract

It was established that distribution of the near-zero modes of the Dirac operator is consistent with the Chiral Random Matrix Theory (CRMT) and can be considered as a consequence of spontaneous breaking of chiral symmetry (SBCS) in QCD. The higher-lying modes of the Dirac operator carry information about confinement physics and are not affected by SBCS. We study distributions of the near-zero and higher-lying modes of the overlap Dirac operator within $N_F=2$ dynamical simulations. We find that distributions of both near-zero and higher-lying modes are the same and follow the Gaussian Unitary Ensemble of Random Matrix Theory. This means that randomness, while consistent with SBCS, is not a consequence of SBCS and is related to some more general property of QCD in confinement regime.

Comments: Contribution to Lattice 2017 proceedings, 18-24 June, 2017, Granada, Spain