Spectrum of the Dirac operator in a QCD instanton liquid: two versus three colors

Abstract

Approximating the sum over all gauge field configurations in the QCD partition function by a liquid of instantons, we calculate the spectrum of the Dirac operator for two and three colors and for 0, 1 and 2 flavors. We find a remarkable difference in the spectrum near zero virtuality between 2 and 3 colors, which can be explained in terms of chiral random matrix theory. For two colors the Dirac operator is real, and the appropriate random matrix ensemble has real matrix elements. For three colors the Dirac operator is complex, and the spectrum can be described by a random matrix ensemble with complex matrix elements. These results provide further evidence that the spectrum near zero virtuality is universal and is completely determined by symmetries.

12 pages and 2 figures (available on request), SUNY-NTG-94/6

References in corpus (4)

• Random matrix theory and spectral sum rules for the Dirac operator in QCD
• The spectrum of the QCD Dirac operator and chiral random matrix theory: the threefold way
• Spectral Density of the QCD Dirac Operator near Zero Virtuality
• The spectrum of the Dirac operator near zero virtuality for $N_c=2$

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• Eigenvalue spectra of QCD and the fate of $U_A(1)$ breaking towards the chiral limit
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• Exploring the Chiral Regime of QCD in the Interacting Instanton Liquid Model
• Eigenvalues of the QCD Dirac matrix with improved staggered quarks in the continuum limit
• Virasoro Constraints and Flavor-Topology Duality in QCD
• Microscopic spectral density in random matrix models for chiral and diquark condensation
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