Equivalence of Matrix Models for Complex QCD Dirac Spectra

TL;DR

This paper demonstrates the equivalence of two matrix models for complex QCD Dirac spectra in the broken chiral symmetry phase, providing insights into spectral correlations and the QCD phase diagram.

Contribution

It establishes an exact equivalence between two different matrix models for QCD with chemical potential, linking a QCD-related model to a calculable spectral correlation model.

Findings

Models are equivalent in the broken phase with weak non-Hermiticity.

The equivalence is valid at strong non-Hermiticity for small chemical potential.

Predictions from the models are compared to lattice QCD eigenvalues.

Abstract

Two different matrix models for QCD with a non-vanishing quark chemical potential are shown to be equivalent by mapping the corresponding partition functions. The equivalence holds in the phase with broken chiral symmetry. It is exact in the limit of weak non-Hermiticity, where the chemical potential squared is rescaled with the volume. At strong non-Hermiticity it holds only for small chemical potential. The first model proposed by Stephanov is directly related to QCD and allows to analyze the QCD phase diagram. In the second model suggested by the author all microscopic spectral correlation functions of complex Dirac operators can be calculated in the broken phase. We briefly compare those predictions to complex Dirac eigenvalues from quenched QCD lattice simulations.