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

TL;DR

This paper investigates the spectral differences of the Dirac operator in a QCD instanton liquid model for two and three colors, revealing symmetry-based universality in the near-zero spectrum.

Contribution

It demonstrates how the Dirac spectrum varies between two and three color QCD and explains these differences using chiral random matrix theory.

Findings

Spectral differences near zero virtuality between 2 and 3 colors.

Real vs. complex Dirac operators correspond to different random matrix ensembles.

Spectrum near zero is universal and dictated by symmetries.

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.