An Itzykson-Zuber-like Integral and Diffusion for Complex Ordinary and Supermatrices

Abstract

We compute an analogue of the Itzykson-Zuber integral for the case of arbitrary complex matrices. The calculation is done for both ordinary and supermatrices by transferring the Itzykson-Zuber diffusion equation method to the space of arbitrary complex matrices. The integral is of interest for applications in Quantum Chromodynamics and the theory of two-dimensional Quantum Gravity.

20 pages, RevTeX, no figures, agrees with published version, including "Note added in proof" with an additional result for rectangular supermatrices

References in corpus (5)

• Random matrix model of QCD at finite density and the nature of the quenched limit
• A random matrix model for chiral symmetry breaking
• Chiral symmetry at finite T, the phase of the Polyakov loop and the spectrum of the Dirac operator
• The chiral phase transition in a random matrix model with molecular correlations
• The Itzykson-Zuber Integral for U(m|n)

Cited by in corpus (47)

• Random Matrix Theory and Chiral Symmetry in QCD
• The Microscopic Spectral Density of the QCD Dirac Operator
• From chiral Random Matrix Theory to chiral Perturbation Theory
• BGWM as Second Constituent of Complex Matrix Model
• Character Expansions, Itzykson-Zuber Integrals, and the QCD Partition Function
• The microscopic spectrum of the QCD Dirac operator with finite quark masses
• On some integrals over the U(N) unitary group and their large N limit
• Universal spectral correlations of the Dirac operator at finite temperature
• Matrix Models and QCD with Chemical Potential
• A new Chiral Two-Matrix Theory for Dirac Spectra with Imaginary Chemical Potential
• On the supersymmetric partition function in QCD-inspired random matrix models
• Generalizations of some integrals over the unitary group
• Characteristic polynomials of random Hermitian matrices and Duistermaat-Heckman localisation on non-compact Kaehler manifolds
• Beyond universality in random matrix theory
• Universality of Correlation Functions in Random Matrix Models of QCD
• On correlation functions of characteristic polynomials for chiral Gaussian Unitary Ensemble
• The Wilson Dirac Spectrum for QCD with Dynamical Quarks
• Chiral Random Matrix Model for Critical Statistics
• Microscopic Spectrum of the QCD Dirac Operator in Three Dimensions
• On matrix model partition functions for QCD with chemical potential
• Character Expansions for the Orthogonal and Symplectic Groups
• Optimal Lower Bound on the Least Singular Value of the Shifted Ginibre Ensemble
• Spectral correlations of the massive QCD Dirac operator at finite temperature
• Polynomial Ensembles and Pólya Frequency Functions
• Stressed Cooper pairing in QCD at high isospin density: effective Lagrangian and random matrix theory
• Distribution of the local density of states, reflection coefficient and Wigner delay time in absorbing ergodic systems at the point of chiral symmetry
• Coherent state operators, giant gravitons, and gauge-gravity correspondence
• Hydrodynamical spectral evolution for random matrices
• GUE-chGUE Transition preserving Chirality at finite Matrix Size
• Character expansion method for supergroups and extended superversions of the Leutwyler-Smilga and Berezin-Karpelevich integrals
• Additive Matrix Convolutions of Pólya Ensembles and Polynomial Ensembles
• Density of State in a Complex Random Matrix Theory with External Source
• Partially quenched chiral perturbation theory in the epsilon regime at next-to-leading order
• On the Efetov-Wegner terms by diagonalizing a Hermitian supermatrix
• Derivative principles for invariant ensembles
• Singular values for products of two coupled random matrices: hard edge phase transition
• On Hubbard-Stratonovich Transformations over Hyperbolic Domains
• Supersymmetry for disordered systems with interaction
• Symmetry Crossover Protecting Chirality in Dirac Spectra
• Finite rank perturbations in products of coupled random matrices: From one correlated to two Wishart ensembles
• Unitary matrix integral for QCD with real quarks and the GOE-GUE crossover
• Randomness on the Lattice
• Superbosonization in disorder and chaos: The role of anomalies
• Individual eigenvalue distributions of crossover chiral random matrices and low-energy constants of SU(2)$\times$U(1) lattice gauge theory
• Universal microscopic spectrum of the unquenched QCD Dirac operator at finite temperature
• Janossy densities for chiral random matrix ensembles and their applications to two-color QCD
• Quantum chaos in 2D gravity