Distribution of the Dirac modes in QCD

TL;DR

This paper investigates the distribution of Dirac operator modes in QCD, revealing that both near-zero and higher-lying modes follow the Gaussian Unitary Ensemble of Random Matrix Theory, indicating a broader origin of randomness beyond chiral symmetry breaking.

Contribution

The study demonstrates that the distributions of both near-zero and higher-lying Dirac modes in QCD are identical and follow RMT, suggesting randomness is not solely due to chiral symmetry breaking.

Findings

Both mode types follow Gaussian Unitary Ensemble distribution.

Randomness in Dirac modes is not a consequence of chiral symmetry breaking.

Distributions are consistent across different mode types 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.