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 higherlying 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 NF = 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.
Highlights
The near-zero modes of the Dirac operator in QCD are related to spontaneous breaking of chiral symmetry (SBCS) via the Banks-Casher relation [1]
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
While the lowest-lying modes of the Dirac operator are strongly affected by SBCS, the higher-lying modes are subject to confinement physics
Summary
The near-zero modes of the Dirac operator in QCD are related to spontaneous breaking of chiral symmetry (SBCS) via the Banks-Casher relation [1]. Within the -regime, i.e. when ΛQCDL 1 and mπL 1, where L is the linear size of the lattice and mπ is the pion mass, the Chiral Random Matrix Theory (CRMT) links the distribution law of the near-zero modes of the Dirac operator with the random matrices [3, 4]. While the lowest-lying modes of the Dirac operator are strongly affected by SBCS, the higher-lying modes are subject to confinement physics This was recently observed on the lattice via truncation of the lowest modes of the overlap Dirac operator from quark propagators [7,8,9,10]. Given success of CRMT for the lowest-lying modes of the Dirac operator it is natural to expect that distribution law of the higher-lying modes should be different and should reflect confinement physics. This motivates our study of the distribution of the lowest-lying and higher-lying modes of the Dirac operator and their comparison
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