Chiral random matrix theory and QCD

Details Chiral random matrix theory and QCD Chiral random matrix theory and QCD

1994-05-02

arxiv.org/abs/hep-th/9405006v1

Physics

High Energy Physics

High Energy Physics - Theory

16 pages and 4 figures (available upon request), SUNY-NTG-94/20

Scientific paper

As was shown by Leutwyler and Smilga, the fact that chiral symmetry is broken and the existence of a effective finite volume partition function leads to an infinite number of sum rules for the eigenvalues of the Dirac operator in QCD. In this paper we argue these constraints, together with universality arguments from quantum chaos and universal conductance fluctuations, completely determine its spectrum near zero virtuality. As in the classical random matrix ensembles, we find three universality classes, depedending on whether the color representation of the gauge group is pseudo-real, complex or real. They correspond to $SU(2)$ with fundamental fermions, $SU(N_c)$, $N_c \ge 3$, with fundamental fermions, and $SU(N_c)$, $N_c \ge 3$, with adjoint fermions, respectively.}

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