Spectrum of the QCD Dirac operator and chiral random matrix theory

Journal Article · Mon Apr 18 04:00:00 EDT 1994 · Physical Review Letters; (United States)

DOI:https://doi.org/10.1103/PhysRevLett.72.2531· OSTI ID:7206841

Verbaarschot, J ^[1]

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1. Department of Physics, State University of New York at Stony Brook, Stony Brook, New York 11794 (United States)

We argue that the spectrum of the QCD Dirac operator near zero virtuality can be described by random matrix theory. As in the case of the classical random matrix ensembles of Dyson we have three different cases: the chiral orthogonal ensemble, the chiral unitary ensemble, and the chiral symplectic ensemble. They correspond to gauge groups SU(2) in the fundamental representation, SU([ital N][sub [ital c]]), [ital N][sub [ital c]][ge]3 in the fundamental representation, and non-Abelian gauge groups SU([ital N][sub [ital c]]) for all [ital N][sub [ital c]] with fermions in the adjoint representation, respectively. The joint probability density reproduces Leutwyler-Smilga sum rules.

• DOE Contract Number: FG02-88ER40388
• OSTI ID: 7206841
• Journal Information: Physical Review Letters; (United States), Journal Name: Physical Review Letters; (United States) Vol. 72:16; ISSN 0031-9007; ISSN PRLTAO
• Country of Publication: United States
• Language: English

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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CHIRAL SYMMETRY
DIRAC OPERATORS
EQUATIONS
FIELD THEORIES
FUNCTIONS
GAUGE INVARIANCE
INVARIANCE PRINCIPLES
LIE GROUPS
MATHEMATICAL OPERATORS
PARTITION FUNCTIONS
PROBABILITY
QUANTUM CHROMODYNAMICS
QUANTUM FIELD THEORY
QUANTUM OPERATORS
RANDOMNESS
SPECTRA
SU GROUPS
SU-2 GROUPS
SUM RULES
SYMMETRY
SYMMETRY GROUPS