Chiral Disorder in QCD

Abstract

Using the Gell-Mann-Oakes-Renner (GOR) relation and semi-classical arguments, we show that the bulk quark spectrum in QCD exhibits a variety of regimes including the ergodic one described by random matrix theory. We analyze the quark spectral form-factor in the diffusive and ballistic regime. We suggest that a class of chiral transitions in QCD is possibly of the metal-insulator type, with a universal spectral statistics at the mobility edge.

References in corpus (1)

• Thouless Energy and Correlations of QCD Dirac Eigenvalues

Cited by in corpus (48)

• Random Matrix Theory and Chiral Symmetry in QCD
• Instantons at work
• From chiral Random Matrix Theory to chiral Perturbation Theory
• Localization in Lattice QCD
• Thouless Energy and Correlations of QCD Dirac Eigenvalues
• Chiral phase transition in lattice QCD as a metal-insulator transition
• Eigenvalue tunnelling and decay of quenched random networks
• Small eigenvalues of the SU(3) Dirac operator on the lattice and in Random Matrix Theory
• The Spectral Density of the QCD Dirac Operator and Patterns of Chiral Symmetry Breaking
• Eigenvalue spectrum of massless Dirac operators on the lattice
• Modeling Finite-Volume Effects and Chiral Symmetry Breaking in Two-Flavor QCD Thermodynamics
• Disorder in the Sachdev-Yee-Kitaev Model
• Chiral phase transition and Anderson localization in the Instanton Liquid Model for QCD
• Pion and Kaon parton distributions in the QCD instanton vacuum
• Microscopic correlations of non-Hermitian Dirac operators in three-dimensional QCD
• Spectral ergodicity and normal modes in ensembles of sparse matrices
• Statistical analysis and the equivalent of a Thouless energy in lattice QCD Dirac spectra
• Critical Scaling at Zero Virtuality in QCD
• Localization of Dirac Fermions in Finite-Temperature Gauge Theory
• Deconfinement, chiral transition and localisation in a QCD-like model
• Microscopic Universality and the Chiral Phase Transition in two Flavor QCD
• Random Matrix Theory, Chiral Perturbation Theory, and Lattice Data
• Character Expansions for the Orthogonal and Symplectic Groups
• Rotating Dirac fermions in a magnetic field in 1+2,3 dimensions
• Spectral correlations of the massive QCD Dirac operator at finite temperature
• Spectrum of the U(1) staggered Dirac operator in four dimensions
• Stochastic field theory for a Dirac particle propagating in gauge field disorder
• Burgers-like equation for spontaneous breakdown of the chiral symmetry in QCD
• The QCD vacuum as a disordered medium: A simplified model for the QCD Dirac operator
• Handbook Article on Applications of Random Matrix Theory to QCD
• Thouless energy in QCD and effects of diffusion modes on level correlations of Dirac operator
• Universality crossover between chiral random matrix ensembles and twisted SU(2) lattice Dirac spectra
• Semiclassical limits for the QCD Dirac operator
• Chiral Disorder and QCD Phase Transitions
• Spectrum of the SU(3) Dirac operator on the lattice: Transition from random matrix theory to chiral perturbation theory
• Drag Force in the Vacuum of Confining Gauge Theories
• Dirac eigenvalues and eigenvectors at finite temperature
• Metal or Insulator? Dirac operator spectrum in holographic QCD
• The zeros of the QCD partition function
• Universal and non-universal behavior in Dirac spectra
• Chiral Disorder and QCD at Finite Chemical Potential
• Hydrodynamics of the Chiral Dirac Spectrum
• Random Matrix Model for Wilson Fermions on the Lattice
• Chiral Disorder in Two-Color QCD with Abelian External Fluxes
• Beyond the Thouless energy
• Triage of the Sign Problem
• Chiral Random Matrix Model at Finite Chemical Potential: Characteristic Determinant and Edge Universality
• Hydrodynamical Description of the QCD Dirac Spectrum at Finite Chemical Potential