Spectral Density of the QCD Dirac Operator near Zero Virtuality

TL;DR

This paper analyzes the spectral density of the QCD Dirac operator near zero virtuality using a random matrix model, deriving exact formulas that connect to QCD sum rules and low-energy behavior.

Contribution

It provides exact spectral density and correlation functions for a random matrix model representing low-energy QCD, including universal microscopic limits.

Findings

Exact spectral density derived for arbitrary flavors

Pair correlation functions obtained explicitly

Microscopic limits yield universal sum rules

Abstract

We investigate the spectral properties of a random matrix model, which in the large $N$ limit, embodies the essentials of the QCD partition function at low energy. The exact spectral density and its pair correlation function are derived for an arbitrary number of flavors and zero topological charge. Their microscopic limit provide the master formulae for sum rules for the inverse powers of the eigenvalues of the QCD Dirac operator as recently discussed by Leutwyler and Smilga.