Spectra of massive QCD Dirac Operators from Random Matrix Theory: all three chiral symmetry breaking patterns

TL;DR

This paper uses Random Matrix Theory to unify and analyze the spectral correlations of QCD Dirac operators across all three chiral symmetry breaking patterns, providing a comprehensive framework and validating universality with lattice data.

Contribution

It presents a unified RMT approach to describe massive QCD Dirac spectra for all three symmetry classes, explicitly proving universality.

Findings

Universal spectral correlation functions for all three classes.

Validation of RMT predictions with lattice data for β=4.

A unifying framework for chiral symmetry breaking patterns.

Abstract

The microscopic spectral eigenvalue correlations of QCD Dirac operators in the presence of dynamical fermions are calculated within the framework of Random Matrix Theory (RMT). Our approach treats the low--energy correlation functions of all three chiral symmetry breaking patterns (labeled by the Dyson index $\beta=1,2$ and 4) on the same footing, offering a unifying description of massive QCD Dirac spectra. RMT universality is explicitly proven for all three symmetry classes and the results are compared to the available lattice data for $\beta=4$.