Chiral Symmetry and the Low-Energy Spectrum of the QCD Dirac Operator

Details Chiral Symmetry and the Low-Energy Spectrum of the QCD Dirac Operator Chiral Symmetry and the Low-Energy Spectrum of the QCD Dirac Operator

1999-12-22

arxiv.org/abs/hep-ph/9912479v1

Nucl.Phys. A663 (2000) 1023-1026

Physics

High Energy Physics

High Energy Physics - Phenomenology

Invited talk at XVth PANIC conference, June 10-16, Uppsala, 5 pages, Latex

Scientific paper

10.1016/S0375-9474(99)00760-5

The order parameter of the chiral phase transition is directly related to the infrared part of the spectrum of the QCD Dirac operator. This part of the spectrum follows from the low energy limit of QCD which is given by a partition function of weakly interacting Goldstone modes. We find that the slope of the Dirac spectrum is determined by the pion decay constant whereas for $\lambda \ll 1/L^2 \Lambda_{\rm QCD}$ the correlations of the Dirac eigenvalues are given by a random matrix theory with the global symmetries of the QCD partition function. A possible observation of these continuum results in lattice QCD with staggered fermions is discussed.

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