Spectral sum rules and Selberg's integral

Abstract

Using Selberg's integral formula we derive all Leutwyler-Smilga type sum rules for one and two flavors, and for each of the three chiral random matrix ensembles. In agreement with arguments from effective field theory, all sum rules for $N_f=1$ coincide for the three ensembles. The connection between spectral correlations and the low-energy effective partition function is discussed.

10 pages, SUNY-NTG-94/6

References in corpus (3)

• Random matrix theory and spectral sum rules for the Dirac operator in QCD
• Spectral Density of the QCD Dirac Operator near Zero Virtuality
• The spectrum of the Dirac operator near zero virtuality for $N_c=2$

Cited by in corpus (50)

• Random Matrix Theory and Chiral Symmetry in QCD
• Biorthogonal ensembles
• The Microscopic Spectral Density of the QCD Dirac Operator
• From chiral Random Matrix Theory to chiral Perturbation Theory
• Microscopic universality in the spectrum of the lattice Dirac operator
• Finite volume partition functions and Itzykson-Zuber integrals
• Universal fluctuations in spectra of the lattice Dirac operator
• A random matrix model for chiral symmetry breaking
• Smallest Dirac Eigenvalue Distribution from Random Matrix Theory
• Universal Spectral Correlators and Massive Dirac Operators
• Universal scaling of the valence quark mass dependence of the chiral condensate
• Thermodynamics of chiral symmetry at low densities
• Thouless Energy and Correlations of QCD Dirac Eigenvalues
• Multicritical Microscopic Spectral Correlators of Hermitian and Complex Matrices
• Effective Lagrangians and Chiral Random Matrix Theory
• Universality in Chiral Random Matrix Theory at $\beta =1$ and $\beta =4$
• Thouless Energy and Correlations of QCD Dirac Eigenvalues
• Universality near zero virtuality
• The Spectral Density of the QCD Dirac Operator and Patterns of Chiral Symmetry Breaking
• Random matrix model for chiral symmetry breaking and color superconductivity in QCD at finite density
• Random matrix study of the phase structure of QCD with two colors
• Exact moments of the Sachdev-Ye-Kitaev model up to order $1/N^2$
• Microscopic Spectra of Dirac Operators and Finite-Volume Partition Functions
• Volume behaviour of quark condensate, pion mass and decay constant from Dyson-Schwinger equations
• Universal Massive Spectral Correlators and QCD_3
• Universal Scaling of the Chiral Condensate in Finite-Volume Gauge Theories
• Eigenvalue Distributions of the QCD Dirac Operator
• Spectral Sum Rules of the Dirac operator and Partially Quenched Chiral Condensates
• Topology and the Dirac Operator Spectrum in Finite-Volume Gauge Theories
• Universality of Correlation Functions in Random Matrix Models of QCD
• Low-lying Eigenvalues of the QCD Dirac Operator at Finite Temperature
• Staggered Fermions and Gauge Field Topology
• Random matrix model approach to chiral symmetry
• A Random Matrix Model for Color Superconductivity at Zero Chemical Potential
• On Finite-Volume Gauge Theory Partition Functions
• The orthogonal ensemble of random matrices and QCD in three dimensions
• Random Matrices and the Convergence of Partition Function Zeros in Finite Density QCD
• Large $N$ expansion of the moments and free energy of Sachdev-Ye-Kitaev model, and the enumeration of intersection graphs
• Polyakov loops and spectral properties of the staggered Dirac operator
• Virasoro Constraints and Flavor-Topology Duality in QCD
• Logarithmic Universality in Random Matrix Theory
• Sum Rules for the Dirac Spectrum of the Schwinger Model
• Supersymmetry Method for Chiral Random Matrix Theory with Arbitrary Rotation Invariant Weights
• The Asymptotics of Quantum Max-Flow Min-Cut
• Chiral Random Matrix Theory and Chiral Perturbation Theory
• Random Matrix Theory and QCD at nonzero chemical potential
• Microscopic spectral density in random matrix models for chiral and diquark condensation
• Chiral condensate of lattice QCD with massless quarks from the probability distribution function method
• Eigenmodes of the Dirac Operator and Chiral Properties of QCD with Sea Quarks
• On the evaluation of some Selberg-like integrals