The solution of a chiral random matrix model with complex eigenvalues

TL;DR

This paper extends the chiral Gaussian Unitary Ensemble into the complex plane, deriving correlation functions for finite and large N, and explores the transition from chGUE to a generalized Ginibre ensemble with applications to QCD.

Contribution

It provides a detailed solution to the complex extension of the chGUE, including new correlation functions and analysis of the non-Hermitian transition.

Findings

Derived correlation functions for finite N complex eigenvalues.

Established the transition from chGUE to a generalized Ginibre ensemble.

Discussed implications for QCD eigenvalue spectra with chemical potential.

Abstract

We describe in detail the solution of the extension of the chiral Gaussian Unitary Ensemble (chGUE) into the complex plane. The correlation functions of the model are first calculated for a finite number of N complex eigenvalues, where we exploit the existence of orthogonal Laguerre polynomials in the complex plane. When taking the large-N limit we derive new correlation functions in the case of weak and strong non-Hermiticity, thus describing the transition from the chGUE to a generalized Ginibre ensemble. Applications to the Dirac operator eigenvalue spectrum in QCD with non-vanishing chemical potential are briefly discussed. This is an extended version of arXiv:hep-th/0204068.