Microscopic correlation functions for the QCD Dirac operator with chemical potential

TL;DR

This paper introduces a chiral random matrix model with complex eigenvalues to predict local fluctuations of Dirac operator eigenvalues in QCD with non-zero chemical potential, providing explicit correlation functions.

Contribution

It derives new correlation functions for complex Dirac eigenvalues, linking non-Hermiticity to chemical potential and analyzing spectral correlations in different phases.

Findings

Correlation functions for complex eigenvalues derived

Spectral correlations depend on quark flavors and chemical potential

Explicit formulas provided for finite and large matrix sizes

Abstract

A chiral random matrix model with complex eigenvalues is solved as an effective model for QCD with non-vanishing chemical potential. We derive new matrix model correlation functions which predict the local fluctuations of complex Dirac operator eigenvalues at zero virtuality. The parameter which measures the non-Hermiticity of the Dirac matrix is identified with the chemical potential. In the phase with broken chiral symmetry all spectral correlations of the Dirac eigenvalues are calculated as functions of quark flavors and chemical potential. The derivation uses the orthogonality of the Laguerre polynomials in the complex plane. Explicit results are given for any finite matrix size N as well in the large-N limit for weak and strong non-Hermiticity.