The spectrum of the QCD Dirac operator and chiral random matrix theory: the threefold way

Details The spectrum of the QCD Dirac operator and chiral random matrix theory: the threefold way The spectrum of the QCD Dirac operator and chiral random matrix theory: the threefold way

1994-01-13

arxiv.org/abs/hep-th/9401059v1

Phys.Rev.Lett.72:2531-2533,1994

Physics

High Energy Physics

High Energy Physics - Theory

7 pages, SUNY-NTG-94/1

Scientific paper

10.1103/PhysRevLett.72.2531

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 classical random matrix ensembles of Dyson we have three distinct classes: the chiral orthogonal ensemble (chGOE), the chiral unitary ensemble (chGUE) and the chiral symplectic ensemble (chGSE). They correspond to gauge groups $SU(2)$ in the fundamental representation, $SU(N_c), N_c \ge 3$ in the fundamental representation, and gauge groups for all $N_c$ in the adjoint representation, respectively. The joint probability density reproduces Leutwyler-Smilga sum rules.

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