Lattice QCD with Ginsparg-Wilson fermions

Abstract

Lattice QCD using fermions whose Dirac operator obeys the Ginsparg-Wilson relation, is perhaps the best known formulation of QCD with a finite cutoff. It reproduces all the low energy QCD phenomenology associated with chiral symmetry at finite lattice spacings. In particular it explains the origin of massless pions due to spontaneous chiral symmetry breaking and leads to new ways to approach the U(1) problem on the lattice. Here we show these results in the path integral formulation and derive for the first time in lattice QCD a known formal continuum relation between the chiral condensate and the topological susceptibility. This relation leads to predictions for the critical behavior of the topological susceptibility near the phase transition and can now be checked in Monte-Carlo simulations even at finite lattice spacings.

6 pages, REVTEX. Added a new section on the critical behavior of the zero modes near T_c with various flavors. This version will appear in Phys. Rev. D

References in corpus (10)

• Exact chiral symmetry on the lattice and the Ginsparg-Wilson relation
• The index theorem in QCD with a finite cut-off
• Spontaneous Flavor and Parity Breaking with Wilson Fermions
• Vector like gauge theories with almost massless fermions on the lattice
• Lattice QCD without tuning, mixing and current renormalization
• Spectral flow, condensate and topology in lattice QCD
• Topological Charge and The Spectrum of Exactly Massless Fermions on the Lattice
• Anomalous Chiral Symmetry Breaking above the QCD Phase Transition
• Topology, fermionic zero modes and flavor singlet correlators in finite temperature QCD
• Dynamical QCD thermodynamics with domain wall fermions

Cited by in corpus (47)

• Locality properties of Neuberger's lattice Dirac operator
• Theta dependence of SU(N) gauge theories in the presence of a topological term
• Deconfinement transition in two-flavour lattice QCD with dynamical overlap fermions in an external magnetic field
• Testing the fixed-point QCD action and the construction of chiral currents
• Aspects of Chiral Symmetry and the Lattice
• Precision study of the SU(3) topological susceptibility in the continuum
• Finite-size scaling of the quark condensate in quenched lattice QCD
• Solutions of the Ginsparg-Wilson Relation
• An Introduction to Chiral Symmetry on the Lattice
• Chiral Symmetry, Quark Mass, and Scaling of the Overlap Fermions
• Topological Susceptibility to the One-Loop Order in Chiral Perturbation Theory
• One-loop renormalization of fermionic currents with the overlap-Dirac operator
• Axial vector current of exact chiral symmetry on the lattice
• Lattice QCD with the Overlap-Dirac Operator: Its $\Lambda$ Parameter, and One-Loop Renormalization of Fermionic Currents
• Accelerated Overlap Fermions
• Witten-Veneziano Relation, Quenched QCD, and Overlap Fermions
• Lattice chiral symmetry, Yukawa couplings and the Majorana condition
• Convergence Rate and Locality of Improved Overlap Fermions
• Lattice Chiral Symmetry and the Wess-Zumino Model
• Heavy and Light Quarks with Lattice Chiral Fermions
• Relation $Tr{\gamma }_5=0$ and the index theorem in lattice gauge theory
• Lambda-parameter of lattice QCD with the overlap-Dirac operator
• Confinement, chiral symmetry, and the lattice
• Axial anomaly with the overlap-Dirac operator in arbitrary dimensions
• Lattice 2001: Reflections
• Quenched QCD at finite temperature with chiral Fermions
• Strong Non-Ultralocality of Ginsparg-Wilson Fermionic Actions
• Locality Properties of a New Class of Lattice Dirac Operators
• Topological Phases in Neuberger-Dirac operator
• Flavor symmetry breaking in lattice QCD with a mixed action
• Magnetic catalysis in the (2+1)-dimensional Gross-Neveu model
• Domain wall fermion and CP symmetry breaking
• Chiral Symmetry Breaking and Chiral Polarization: Tests for Finite Temperature and Many Flavors
• Lattice QCD with the Overlap Fermions at Strong Gauge Coupling
• Lattice QCD with the Overlap Fermions at Strong Gauge Coupling (II)
• Gross-Neveu model with overlap fermions
• The magnetized (2+1)-dimensional Gross-Neveu model at finite density
• Color confinement, chiral symmetry breaking, and catalytic effect induced by monopole and instanton creations
• Discretisation effects in the topological susceptibility in lattice QCD
• Monopole and instanton effects in QCD
• Renormalization of lattice field theories with infinite-range wavelets
• Lattice Chiral Symmetry in Fermionic Interacting Theories and the Antifield Formalism
• Fermion determinant and chiral anomaly on a finite lattice
• Monopole and instanton effects on connected and disconnected correlations for scalar density
• Monopoles, spectra of overlap fermions, and eta-prime meson in external magnetic fields
• Gap in the Dirac spectrum and quark propagator symmetries in lattice QCD
• Criterium for the index theorem on the lattice