scholarly journals Spectra of massive QCD Dirac operators from random matrix theory: all three chiral symmetry breaking patterns

2001 ◽  
Vol 94 (1-3) ◽  
pp. 681-684 ◽  
Author(s):  
G. Akemann ◽  
E. Kanzieper
Keyword(s):  
Symmetry Breaking ◽  
Chiral Symmetry ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory ◽  
Chiral Symmetry Breaking ◽  
Dirac Operators

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 Random matrix model for chiral symmetry breaking

1996 ◽  
Vol 53 (12) ◽  
pp. 7223-7230 ◽  
Author(s):  
A. D. Jackson ◽  
J. J. M. Verbaarschot
Keyword(s):  
Symmetry Breaking ◽  
Chiral Symmetry ◽  
Matrix Model ◽  
Random Matrix ◽  
Chiral Symmetry Breaking ◽  
Random Matrix Model

NEARLY CONFORMAL GAUGE THEORIES ON THE LATTICE

2010 ◽  
Vol 25 (27n28) ◽  
pp. 5162-5174 ◽  
Author(s):  
ZOLTÁN FODOR ◽  
KIERAN HOLLAND ◽  
JULIUS KUTI ◽  
DÁNIEL NÓGRÁDI ◽  
CHRIS SCHROEDER
Keyword(s):  
Symmetry Breaking ◽  
Chiral Symmetry ◽  
Gauge Theories ◽  
Matrix Theory ◽  
Chiral Symmetry Breaking ◽  
Chiral Condensate ◽  
Theoretical Understanding ◽  
Conformal Window ◽  
Running Coupling ◽  
Conformal Gauge

We present selected new results on chiral symmetry breaking in nearly conformal gauge theories with fermions in the fundamental representation of the SU (3) color gauge group. We found chiral symmetry breaking (χSB) for all flavors between Nf = 4 and Nf = 12 with most of the results discussed here for Nf = 4, 8, 12 as we approach the conformal window. To identify χSB we apply several methods which include, within the framework of chiral perturbation theory, the analysis of the Goldstone spectrum in the p -regime and the spectrum of the fermion Dirac operator with eigenvalue distributions of random matrix theory in the ϵ-regime. Chiral condensate enhancement is observed with increasing Nf when the electroweak symmetry breaking scale F is held fixed in technicolor language. Important finite-volume consistency checks from the theoretical understanding of the SU(Nf) rotator spectrum of the δ-regime are discussed. We also consider these gauge theories at Nf = 16 inside the conformal window. Our work on the running coupling is presented separately.1

scholarly journals Random Matrix Theory and Chiral Symmetry in QCD

2000 ◽  
Vol 50 (1) ◽  
pp. 343-410 ◽  
Author(s):  
J.J.M. Verbaarschot ◽  
T. Wettig
Keyword(s):  
Partition Function ◽  
Dirac Operator ◽  
Chiral Symmetry ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory ◽  
Low Energy ◽  
Spontaneous Breaking ◽  
Schematic Model ◽  
Qcd Phase Diagram

▪ Abstract  Random matrix theory is a powerful way to describe universal correlations of eigenvalues of complex systems. It also may serve as a schematic model for disorder in quantum systems. In this review, we discuss both types of applications of chiral random matrix theory to the QCD partition function. We show that constraints imposed by chiral symmetry and its spontaneous breaking determine the structure of low-energy effective partition functions for the Dirac spectrum. We thus derive exact results for the low-lying eigenvalues of the QCD Dirac operator. We argue that the statistical properties of these eigenvalues are universal and can be described by a random matrix theory with the global symmetries of the QCD partition function. The total number of such eigenvalues increases with the square root of the Euclidean four-volume. The spectral density for larger eigenvalues (but still well below a typical hadronic mass scale) also follows from the same low-energy effective partition function. The validity of the random matrix approach has been confirmed by many lattice QCD simulations in a wide parameter range. Stimulated by the success of the chiral random matrix theory in the description of universal properties of the Dirac eigenvalues, the random matrix model is extended to nonzero temperature and chemical potential. In this way we obtain qualitative results for the QCD phase diagram and the spectrum of the QCD Dirac operator. We discuss the nature of the quenched approximation and analyze quenched Dirac spectra at nonzero baryon density in terms of an effective partition function. Relations with other fields are also discussed.

scholarly journals Perturbation treatment of symmetry breaking within random matrix theory

2008 ◽  
Vol 372 (29) ◽  
pp. 4898-4901 ◽  
Author(s):  
J.X. de Carvalho ◽  
M.S. Hussein ◽  
M.P. Pato ◽  
A.J. Sargeant
Keyword(s):  
Symmetry Breaking ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory
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