Quark spectra, topology and random matrix theory

Abstract

Quark spectra in QCD are linked to fundamental properties of the theory including the identification of pions as the Goldstone bosons of spontaneously broken chiral symmetry. The lattice Overlap-Dirac operator provides a nonperturbative, ultraviolet-regularized description of quarks with the correct chiral symmetry. Properties of the spectrum of this operator and their relation to random matrix theory are studied here. In particular, the predictions from chiral random matrix theory in topologically non-trivial gauge field sectors are tested for the first time.

4 pages, revtex, 2 postscript figures. Added a reference

References in corpus (16)

• Exactly massless quarks on the lattice
• From chiral Random Matrix Theory to chiral Perturbation Theory
• Microscopic universality in the spectrum of the lattice Dirac operator
• A Study of Practical Implementations of the Overlap-Dirac Operator in Four Dimensions
• Smallest Dirac Eigenvalue Distribution from Random Matrix Theory
• Universality in Chiral Random Matrix Theory at $\beta =1$ and $\beta =4$
• Small eigenvalues of the SU(3) Dirac operator on the lattice and in Random Matrix Theory
• Dirac Operator Spectra from Finite-Volume Partition Functions
• Microscopic Spectral Density of the Dirac Operator in Quenched QCD
• Microscopic Spectra of Dirac Operators and Finite-Volume Partition Functions
• Microscopic universality with dynamical fermions
• Consistency Conditions for Finite-Volume Partition Functions
• Evidence for fractional topological charge in SU(2) pure Yang-Mills theory
• Topology, fermionic zero modes and flavor singlet correlators in finite temperature QCD
• Explicitly real form of the Wilson-Dirac matrix for SU(2)
• Study of the chiral behavior of [the chiral condensate] in quenched QCD

Cited by in corpus (83)

• Random Matrix Theory and Chiral Symmetry in QCD
• Numerical techniques for lattice QCD in the $\epsilon$--regime
• Non-Hermitian Random Matrix Theory and Lattice QCD with Chemical Potential
• Low-energy couplings of QCD from current correlators near the chiral limit
• Lattice QCD in the epsilon-regime and random matrix theory
• The Index Theorem and Universality Properties of the Low-lying Eigenvalues of Improved Staggered Quarks
• A variant approach to the overlap action
• Two-flavor lattice QCD simulation in the epsilon-regime with exact chiral symmetry
• Finite-size scaling of the quark condensate in quenched lattice QCD
• Low-lying fermion modes, topology and light hadrons in quenched QCD
• Two-flavor lattice QCD in the epsilon-regime and chiral Random Matrix Theory
• Chiral phase transition in lattice QCD as a metal-insulator transition
• Matrix Models and QCD with Chemical Potential
• Finite-size Scaling of Meson Propagators
• Overlap Dirac operator at nonzero chemical potential and random matrix theory
• Quark condensate in two-flavor QCD
• The Low-Lying Dirac Spectrum of Staggered Quarks
• The Scaling of Exact and Approximate Ginsparg-Wilson Fermions
• The Spectral Density of the QCD Dirac Operator and Patterns of Chiral Symmetry Breaking
• A comprehensive picture of topological excitations in finite temperature lattice QCD
• Concerning the quark condensate
• Distributions of Dirac Operator Eigenvalues
• Chiral properties of SU(3) sextet fermions
• Properties of near-zero modes and chiral symmetry breaking
• Finite-Size Scaling of Vector and Axial Current Correlators
• Effective Low Energy Theories and QCD Dirac Spectra
• Spectral Properties of the Overlap Dirac Operator in QCD
• QCD Dirac operator at nonzero chemical potential: lattice data and matrix model
• Universal Scaling of the Chiral Condensate in Finite-Volume Gauge Theories
• Spectra of massive and massless QCD Dirac operators: A novel link
• Eigenvalue Distributions of the QCD Dirac Operator
• Random Matrix Theory for the Hermitian Wilson Dirac Operator and the chGUE-GUE Transition
• Chiral properties of two-flavor QCD in small volume and at large lattice spacing
• Parameters of the lowest order chiral Lagrangian from fermion eigenvalues
• Low-lying Eigenvalues of the QCD Dirac Operator at Finite Temperature
• Microscopic correlation functions for the QCD Dirac operator with chemical potential
• Staggered Fermions and Gauge Field Topology
• Chiral Random Matrix Model for Critical Statistics
• Extracting $F_{\pi }$ from small lattices: unquenched results
• Probing the chiral regime of Nf=2 QCD with mixed actions
• Spectral properties of the Wilson Dirac operator in the $\epsilon$-regime
• Quark spectra and light hadron phenomenology from overlap fermions with improved gauge field action
• Microscopic Universality and the Chiral Phase Transition in two Flavor QCD
• Finite Volume Scaling of Pseudo Nambu-Goldstone Bosons in QCD
• Spectral Universality of Real Chiral Random Matrix Ensembles
• Patterns of Spontaneous Chiral Symmetry Breaking in Vectorlike Gauge Theories
• Unquenched complex Dirac spectra at nonzero chemical potential: two-colour QCD lattice data versus matrix model
• Another determination of the quark condensate from an overlap action
• A Wigner Surmise for Hermitian and Non-Hermitian Chiral Random Matrices
• Completing the picture for the smallest eigenvalue of real Wishart matrices
• Spectrum of the U(1) staggered Dirac operator in four dimensions
• Exact Zero-Modes of the Compact QED Dirac Operator
• Small eigenvalues of the staggered Dirac operator in the adjoint representation and Random Matrix Theory
• Individual complex Dirac eigenvalue distributions from random matrix theory and comparison to quenched lattice QCD with a quark chemical potential
• Effects of Topology in the Dirac Spectrum of Staggered Fermions
• A Numerical Study of the 2-Flavour Schwinger Model with Dynamical Overlap Hypercube Fermions
• Polyakov loops and spectral properties of the staggered Dirac operator
• Effect of low-lying fermion modes in the $\epsilon$-regime of QCD
• Peculiarities in the Spectrum of the Adjoint Scalar Kinetic Operator in Yang-Mills Theory
• Instantons and Chiral Symmetry on the Lattice
• 2+1 Flavor QCD simulated in the epsilon-regime in different topological sectors
• Individual Eigenvalue Distributions of Chiral Random Two-Matrix Theory and the Determination of F_pi
• Chiral Random Matrix Theory and Chiral Perturbation Theory
• Divergent chiral condensate in the quenched Schwinger model
• Approaching $SU(2)$ gauge dynamics with smeared $Z(2)$ vortices
• Monopole and instanton effects in QCD
• Spectra of massive QCD Dirac Operators from Random Matrix Theory: all three chiral symmetry breaking patterns
• Index Theorem and Random Matrix Theory for Improved Staggered Quarks
• The zeros of the QCD partition function
• The Index Theorem and Random Matrix Theory for Improved Staggered Quarks
• Looking for Effects of Topology in the Dirac Spectrum of Staggered Fermions
• Randomness on the Lattice
• Heavy Meson Masses in the ε-Regime of HMχPT
• Distribution law of the Dirac eigenmodes in QCD
• Chiral symmetry breaking from Ginsparg-Wilson fermions
• High temperature meson propagators with domain-wall quarks
• Topology and chiral symmetry in finite temperature QCD
• Universal microscopic spectrum of the unquenched QCD Dirac operator at finite temperature
• Finite-volume meson propagators in quenched chiral perturbation theory
• Janossy densities for chiral random matrix ensembles and their applications to two-color QCD
• Wilson chiral perturbation theory for dynamical twisted mass fermions vs lattice data - a case study
• Finite-Volume Scaling of the Quenched Chiral Condensate
• Overlap Dirac Operator, Eigenvalues and Random Matrix Theory