The solution of a chiral random matrix model with complex eigenvalues

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.

17 pages, 4 figures

References in corpus (6)

• Lattice determination of the critical point of QCD at finite T and μ
• Eigenvalue correlations in non-Hermitean symplectic random matrices
• Boundary states for WZW models
• Microscopic correlations of non-Hermitian Dirac operators in three-dimensional QCD
• Microscopic correlation functions for the QCD Dirac operator with chemical potential
• New Multicritical Random Matrix Ensembles

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• Chiral Symmetry Breaking and the Dirac Spectrum at Nonzero Chemical Potential
• The Complex Laguerre Symplectic Ensemble of Non-Hermitian Matrices
• Matrix Models and QCD with Chemical Potential
• Random matrices beyond the Cartan classification
• Derivation of determinantal structures for random matrix ensembles in a new way
• A new Chiral Two-Matrix Theory for Dirac Spectra with Imaginary Chemical Potential
• QCD Dirac operator at nonzero chemical potential: lattice data and matrix model
• Gap Probabilities in Non-Hermitian Random Matrix Theory
• The Approach to the Thermodynamic Limit in Lattice QCD at μ\neq0
• Random matrix analysis of the QCD sign problem for general topology
• Reconstructing 1/2 BPS Space-Time Metrics from Matrix Models and Spin Chains
• On matrix model partition functions for QCD with chemical potential
• Mixing of orthogonal and skew-orthogonal polynomials and its relation to Wilson RMT
• The chiral Gaussian two-matrix ensemble of real asymmetric matrices
• Individual complex Dirac eigenvalue distributions from random matrix theory and comparison to quenched lattice QCD with a quark chemical potential
• Interpolation between Airy and Poisson statistics for unitary chiral non-Hermitian random matrix ensembles
• Generic critical points of normal matrix ensembles
• Comparing matrix models and QCD lattice data with chemical potential
• Chiral Random Matrix Model at Finite Chemical Potential: Characteristic Determinant and Edge Universality
• Hydrodynamical Description of the QCD Dirac Spectrum at Finite Chemical Potential