Random matrix model approach to chiral symmetry

Details Random matrix model approach to chiral symmetry Random matrix model approach to chiral symmetry

1996-07-31

arxiv.org/abs/hep-lat/9607086v1

Nucl.Phys.Proc.Suppl. 53 (1997) 88-94

Physics

High Energy Physics

High Energy Physics - Lattice

Talk present at LATTICE96(chirality in QCD), plenary session, 7 pages, Latex

Scientific paper

10.1016/S0920-5632(96)00602-0

We review the application of random matrix theory (RMT) to chiral symmetry in QCD. Starting from the general philosophy of RMT we introduce a chiral random matrix model with the global symmetries of QCD. Exact results are obtained for universal properties of the Dirac spectrum: i) finite volume corrections to valence quark mass dependence of the chiral condensate, and ii) microscopic fluctuations of Dirac spectra. Comparisons with lattice QCD simulations are made. Most notably, the variance of the number of levels in an interval containing $n$ levels on average is suppressed by a factor $(\log n)/\pi^2 n$. An extension of the random matrix model model to nonzero temperatures and chemical potential provides us with a schematic model of the chiral phase transition. In particular, this elucidates the nature of the quenched approximation at nonzero chemical potential.

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