The Microscopic Spectral Density of the QCD Dirac Operator

Abstract

We derive the microscopic spectral density of the Dirac operator in $SU(N_c\ge 3)$ Yang-Mills theory coupled to $N_f$ fermions in the fundamental representation. An essential technical ingredient is an exact rewriting of this density in terms of integrations over the super Riemannian manifold $Gl(N_f+1|1)$. The result agrees exactly with earlier calculations based on Random Matrix Theory.

26 pages, Latex

References in corpus (33)

• Riemannian symmetric superspaces and their origin in random matrix theory
• Random matrix theory and spectral sum rules for the Dirac operator in QCD
• The spectrum of the QCD Dirac operator and chiral random matrix theory: the threefold way
• On the Foundations of Chiral Perturbation Theory
• Spectral Density of the QCD Dirac Operator near Zero Virtuality
• Chiral Perturbation Theory for the Quenched Approximation of QCD
• Partially Quenched Gauge Theories and a Application to Staggered Fermions
• Universality of random matrices in the microscopic limit and the Dirac operator spectrum
• From chiral Random Matrix Theory to chiral Perturbation Theory
• Microscopic universality in the spectrum of the lattice Dirac operator
• The spectrum of the Dirac operator near zero virtuality for $N_c=2$
• Finite volume partition functions and Itzykson-Zuber integrals
• Supersymmetry for Systems with Unitary Disorder: Circular Ensembles
• Universal Spectral Correlators and Massive Dirac Operators
• Universal scaling of the valence quark mass dependence of the chiral condensate
• Toward a theory of the integer quantum Hall transition: continuum limit of the Chalker-Coddington model
• Oscillating density of states near zero energy for matrices made of blocks with possible application to the random flux problem
• An Itzykson-Zuber-like Integral and Diffusion for Complex Ordinary and Supermatrices
• The microscopic spectrum of the QCD Dirac operator with finite quark masses
• Effective Lagrangians and Chiral Random Matrix Theory
• Universal spectral correlations of the Dirac operator at finite temperature
• Universality in Chiral Random Matrix Theory at $\beta =1$ and $\beta =4$
• Spectral sum rules and Selberg's integral
• Dirac Operator Spectra from Finite-Volume Partition Functions
• Universality near zero virtuality
• Microscopic Spectra of Dirac Operators and Finite-Volume Partition Functions
• Microscopic universality with dynamical fermions
• Consistency Conditions for Finite-Volume Partition Functions
• The Itzykson-Zuber Integral for U(m|n)
• Dirac spectrum in QCD and Quark Masses
• Universality of Correlation Functions in Random Matrix Models of QCD
• Single-particle Green's functions of the Calogero-Sutherland model at couplings λ= 1/2, 1, and 2
• Massive Spectral Sum Rules for the Dirac Operator

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• Diquark Condensate in QCD with Two Colors at Next-to-Leading Order
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• Singular values of the Dirac operator in dense QCD-like theories
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• Equivalence of QCD in the epsilon-regime and chiral Random Matrix Theory with or without chemical potential
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• Probing the chiral regime of Nf=2 QCD with mixed actions
• Extracting $F_{\pi }$ from small lattices: unquenched results
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• Massive chiral random matrix ensembles at beta = 1 & 4 : Finite-volume QCD partition functions
• Finite Volume Scaling of Pseudo Nambu-Goldstone Bosons in QCD
• Spontaneous chiral symmetry breaking in QCD:a finite-size scaling study on the lattice
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• The Microscopic Twisted Mass Dirac Spectrum
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• Applications of Chiral Perturbation theory to lattice QCD
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• Spectral density of the Hermitean Wilson Dirac operator: a NLO computation in chiral perturbation theory
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• Probing the chiral weak Hamiltonian at finite volumes
• Chiral Random Matrix Theory and Chiral Perturbation Theory
• Handbook Article on Applications of Random Matrix Theory to QCD
• Divergent chiral condensate in the quenched Schwinger model
• Thouless energy in QCD and effects of diffusion modes on level correlations of Dirac operator
• Testing chiral effective theory with quenched lattice QCD
• Quenched penguins and the Delta I=1/2 rule
• Quenched and Unquenched Chiral Perturbation Theory in the ε-Regime
• Individual Eigenvalue Distributions for the Wilson Dirac Operator
• Applicability of the two-particle quantization condition to partially-quenched theories
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