Microscopic correlations of non-Hermitian Dirac operators in three-dimensional QCD

TL;DR

This paper derives explicit formulas for microscopic spectral correlations of non-Hermitian Dirac operators in 3D and 4D QCD, accounting for chemical potential effects and broken flavor symmetry, using a random matrix approach.

Contribution

It provides the first comprehensive analytic expressions for all microscopic k-point correlation functions of complex eigenvalues in non-Hermitian QCD Dirac operators.

Findings

Explicit formulas for all microscopic correlation functions.

Identification of non-Hermiticity parameter with chemical potential effects.

Applicability to both strong and weak non-Hermiticity regimes.

Abstract

In the presence of a non-vanishing chemical potential the eigenvalues of the Dirac operator become complex. We calculate spectral correlation functions of complex eigenvalues using a random matrix model approach. Our results apply to non-Hermitian Dirac operators in three-dimensional QCD with broken flavor symmetry and in four-dimensional QCD in the bulk of the spectrum. The derivation follows earlier results of Fyodorov, Khoruzhenko and Sommers for complex spectra exploiting the existence of orthogonal polynomials in the complex plane. Explicit analytic expressions are given for all microscopic k-point correlation functions in the presence of an arbitrary even number of massive quarks, both in the limit of strong and weak non-Hermiticity. In the latter case the parameter governing the non-Hermiticity of the Dirac matrices is identified with the influence of the chemical potential.