The spectrum of the Dirac operator near zero virtuality for $N_c = 2$

TL;DR

This paper analyzes the spectral properties of the QCD Dirac operator near zero virtuality for two colors, using random matrix theory with real matrix elements to derive analytical spectral density results.

Contribution

It provides an analytical expression for the microscopic spectral density of the Dirac operator for $N_c=2$ using random matrix theory with real matrices.

Findings

Derived an explicit formula for the microscopic spectral density.

Connected spectral density to Leutwyler-Smilga sum rules.

Validated universality of spectral behavior near zero virtuality.

Abstract

We study the spectrum of the QCD Dirac operator near zero virtuality for $N_c =2$. According to a universality argument, it can be described by a random matrix theory with the chiral structure of QCD, but with $real$ matrix elements. Using results derived by Mehta and Mahoux and Nagao and Wadati, we are able to obtain an analytical result for the microscopic spectral density that in turn is the generating function for Leutwyler-Smilga type spectral sum rules.