{
"id": "1709.01886",
"version": "v1",
"published": "2017-09-06T16:40:28.000Z",
"updated": "2017-09-06T16:40:28.000Z",
"title": "Distribution law of the Dirac eigenmodes in QCD",
"authors": [
"M. Catillo",
"L. Ya. Glozman"
],
"categories": [
"hep-lat",
"hep-ph",
"hep-th"
],
"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 $SU(2)_{CS}$ and $SU(2N_F)$ symmetries. We study the distribution of the near-zero and higher-lying eigenmodes of the overlap Dirac operator within $N_F=2$ 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.",
"revisions": [
{
"version": "v1",
"updated": "2017-09-06T16:40:28.000Z"
}
],
"analyses": {
"keywords": [
"distribution law",
"dirac eigenmodes",
"near-zero modes",
"overlap dirac operator",
"random matrix theory"
],
"note": {
"typesetting": "TeX",
"pages": 0,
"language": "en",
"license": "arXiv",
"status": "editable"
}
}
}