Distribution law of the Dirac eigenmodes in QCD
Abstract
The near-zero modes of the Dirac operator are connected to spontaneous breaking of chiral symmetry in QCD (SBCS) via the Banks-Casher relation. At the same time the distribution of the near-zero modes is well described by the Random Matrix Theory (RMT) with the Gaussian Unitary Ensemble (GUE). Then it has become a standard lore that a randomness, as observed through distributions of the near-zero modes of the Dirac operator, is a consequence of SBCS. The higher-lying modes of the Dirac operator are not affected by SBCS and are sensitive to confinement physics and related and symmetries. We study the distribution of the near-zero and higher-lying eigenmodes of the overlap Dirac operator within dynamical simulations. We find that both the distributions of the near-zero and higher-lying modes are perfectly described by GUE of RMT. 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.
Keywords
Cite
@article{arxiv.1709.01886,
title = {Distribution law of the Dirac eigenmodes in QCD},
author = {M. Catillo and L. Ya. Glozman},
journal= {arXiv preprint arXiv:1709.01886},
year = {2018}
}