scholarly journals Spectrum of the SU(3) Dirac operator on the lattice: Transition from random matrix theory to chiral perturbation theory

2002 ◽  
Vol 65 (3) ◽  
Author(s):  
M. Göckeler ◽  
H. Hehl ◽  
P. E. L. Rakow ◽  
A. Schäfer ◽  
T. Wettig
Keyword(s):  
Perturbation Theory ◽  
Dirac Operator ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Chiral Perturbation Theory ◽  
Matrix Theory ◽  
Chiral Perturbation

scholarly journals Random matrix theory, chiral perturbation theory, and lattice data

1999 ◽  
Vol 466 (2-4) ◽  
pp. 293-300 ◽  
Author(s):  
M.E. Berbenni-Bitsch ◽  
M. Göckeler ◽  
H. Hehl ◽  
S. Meyer ◽  
P.E.L. Rakow ◽  
...  
Keyword(s):  
Perturbation Theory ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Chiral Perturbation Theory ◽  
Matrix Theory ◽  
Lattice Data ◽  
Chiral Perturbation

scholarly journals From chiral random matrix theory to chiral perturbation theory

1999 ◽  
Vol 540 (1-2) ◽  
pp. 317-344 ◽  
Author(s):  
J.C. Osborn ◽  
D. Toublan ◽  
J.J.M. Verbaarschot
Keyword(s):  
Perturbation Theory ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Chiral Perturbation Theory ◽  
Matrix Theory ◽  
Chiral Perturbation

Quantum chromodynamics

2018 ◽  
Author(s):  
Marcos Marino
Keyword(s):  
Symmetry Breaking ◽  
Dirac Operator ◽  
Global Symmetries ◽  
Quantum Chromodynamics ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Degrees Of Freedom ◽  
Chemical Potential ◽  
Matrix Theory ◽  
Global Symmetry

This article focuses on chiral random matrix theories with the global symmetries of quantum chromodynamics (QCD). In particular, it explains how random matrix theory (RMT) can be applied to the spectra of the Dirac operator both at zero chemical potential, when the Dirac operator is Hermitian, and at non-zero chemical potential, when the Dirac operator is non-Hermitian. Before discussing the spectra of these Dirac operators at non-zero chemical potential, the article considers spontaneous symmetry breaking in RMT and the QCD partition function. It then examines the global symmetries of QCD, taking into account the Dirac operator for a finite chiral basis, as well as the global symmetry breaking pattern and the Goldstone manifold in chiral random matrix theory (chRMT). It also describes the generating function for the Dirac spectrum and applications of chRMT to QCD to gauge degrees of freedom.

scholarly journals Distribution of the Dirac modes in QCD

2018 ◽  
Vol 175 ◽  
pp. 04005
Author(s):  
M. Catillo ◽  
L. Ya. Glozman
Keyword(s):  
Dirac Operator ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
General Property ◽  
Matrix Theory ◽  
Spontaneous Breaking ◽  
Gaussian Unitary Ensemble ◽  
Zero Modes ◽  
Dynamical Simulations ◽  
Unitary Ensemble

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.

Sign in / Sign up

Export Citation Format

Share Document