Exact chiral symmetry, topological charge and related topics

Abstract

It has been shown recently that Dirac operators satisfying the Ginsparg-Wilson relation provide a solution of the chirality problem in QCD at finite lattice spacing. We discuss different ways to construct these operators and their properties. The possibility to define lattice chiral gauge theories is briefly discussed as well.

15 pages, latex, 3 figures, LATTICE98, plenary talk

References in corpus (3)

• More about exactly massless quarks on the lattice
• The index theorem in QCD with a finite cut-off
• Fractional Inversion in Krylov Space

Cited by in corpus (151)

• The Nf=0 heavy quark potential from short to intermediate distances
• Theta dependence of SU(N) gauge theories in the presence of a topological term
• Chiral symmetry and the Yang--Mills gradient flow
• Magnetic field-induced gluonic (inverse) catalysis and pressure (an)isotropy in QCD
• A new approach to Ginsparg-Wilson fermions
• Chiral perturbation theory at O(a^2) for lattice QCD
• Approximate Ginsparg-Wilson fermions: A first test
• Stability of lattice QCD simulations and the thermodynamic limit
• Weyl fermions on the lattice and the non-abelian gauge anomaly
• Dynamical overlap fermions, results with hybrid Monte-Carlo algorithm
• Testing the fixed-point QCD action and the construction of chiral currents
• Quenched spectroscopy with fixed-point and chirally improved fermions
• Chiral Perturbation Theory for Staggered Sea Quarks and Ginsparg-Wilson Valence Quarks
• Topological vacuum structure of the Schwinger model with matrix product states
• Simulations with different lattice Dirac operators for valence and sea quarks
• Low-Dimensional Long-Range Topological Charge Structure in the QCD Vacuum
• Topological effects in QCD and the problem of short-distance singularities
• Observations on staggered fermions at non-zero lattice spacing
• A variant approach to the overlap action
• Precision study of the SU(3) topological susceptibility in the continuum
• Exploring the structure of the quenched QCD vacuum with overlap fermions
• The U_A(1) Problem on the Lattice with Ginsparg-Wilson Fermions
• Finite-size scaling of the quark condensate in quenched lattice QCD
• Low-lying fermion modes, topology and light hadrons in quenched QCD
• Lattice QCD at finite temperature and density
• Overlap Quark Propagator in Landau Gauge
• Operator improvement for Ginsparg-Wilson fermions
• Axial anomaly and topological charge in lattice gauge theory with Overlap Dirac operator
• Topological charge using cooling and the gradient flow
• Chiral Symmetry, Quark Mass, and Scaling of the Overlap Fermions
• Some more remarks on the Witten-Veneziano formula for the ${\eta }^{\prime }$ mass
• Ginsparg-Wilson Relation, Topological Invariants and Finite Noncommutative Geometry
• Instanton constituents and fermionic zero modes in twisted CP(n) models
• Vacuum structure revealed by over-improved stout-link smearing compared with the overlap analysis for quenched QCD
• One-loop renormalization of fermionic currents with the overlap-Dirac operator
• Lattice QCD with the Overlap-Dirac Operator: Its $\Lambda$ Parameter, and One-Loop Renormalization of Fermionic Currents
• Supersymmetry on the lattice and the Leibniz rule
• Lattice Chiral Gauge Theories
• Lattice fermions with complex mass
• Ginsparg-Wilson Relation and 't Hooft-Polyakov Monopole on Fuzzy 2-Sphere
• Locality with staggered fermions
• Anomaly Cancellation Condition in Lattice Gauge Theory
• Non-perturbative renormalisation and improvement of the local vector current for quenched and unquenched Wilson fermions
• Spectra of massive and massless QCD Dirac operators: A novel link
• Filtered overlap: speedup, locality, kernel non-normality and Z_A~1
• Quark propagator and vertex: systematic corrections of hypercubic artifacts from lattice simulations
• Dynamical generation of a nontrivial index on the fuzzy 2-sphere
• Lattice chiral symmetry, Yukawa couplings and the Majorana condition
• N=2 Wess-Zumino model on the d=2 Euclidean lattice
• Parameters of the lowest order chiral Lagrangian from fermion eigenvalues
• Gauge anomaly cancellations in SU(2)_L \times U(1)_Y Electroweak theory on the lattice
• Topology and higher dimensional representations
• Perturbative Renormalization of Weak-Hamiltonian Four-Fermion Operators with Overlap Fermions
• Calorons and dyons at the thermal phase transition analyzed by overlap fermions
• The Schrödinger functional in lattice QCD with exact chiral symmetry
• Microscopic correlation functions for the QCD Dirac operator with chemical potential
• On Pure Lattice Chern-Simons Gauge Theories
• Chiral Properties of Pseudoscalar Mesons on a Quenched $20^4$ Lattice with Overlap Fermions
• Non-commutative Differential Calculus and the Axial Anomaly in Abelian Lattice Gauge Theories
• Twisted Mass, Overlap and Creutz Fermions: Cut-off Effects at Tree-level of Perturbation Theory
• Chiral Anomaly on Fuzzy 2-Sphere
• Lattice Chiral Symmetry and the Wess-Zumino Model
• The topological structure of SU(2) gluodynamics at T > 0 : an analysis using the Symanzik action and Neuberger overlap fermions
• The dyonic picture of topological objects in the deconfined phase
• Topological susceptibility from twisted mass fermions using spectral projectors and the gradient flow
• Laplacian modes probing gauge fields
• Going chiral: overlap versus twisted mass fermions
• New approximate solutions of the Ginsparg-Wilson equation - tests in 2-d
• Global Anomalies in chiral gauge theories on the lattice
• The chiral limit of the two-flavor lattice Schwinger model with Wilson fermions
• Ginsparg-Wilson Dirac operator in the monopole backgrounds on the fuzzy 2-sphere
• Quantitative comparison of filtering methods in lattice QCD
• Taste-split staggered actions: eigenvalues, chiralities and Symanzik improvement
• Chiral Anomaly and Ginsparg-Wilson Relation on the Noncommutative Torus
• Supersymmetry, chiral symmetry and the generalized BRS transformation in lattice formulations of 4D $\mathcal{N}=1$ SYM
• Isospin-breaking corrections to light-meson leptonic decays from lattice simulations at physical quark masses
• Topology of dynamical lattice configurations including results from dynamical overlap fermions
• New Domain-Wall Fermion Actions
• Lattice 2001: Reflections
• Gauge Field Strength Tensor from the Overlap Dirac Operator
• Ginsparg-Wilson operators and a no-go theorem
• Schwinger Model with the Overlap-Dirac Operator: exact results versus a physics motivated approximation
• CP breaking in lattice chiral gauge theories
• The index of the overlap Dirac operator on a discretized 2d non-commutative torus
• Non-perturbative Renormalization in Lattice Field Theory
• Generalising the Ginsparg-Wilson relation: Lattice Supersymmetry from Blocking Transformations
• Overlap valence quarks on a twisted mass sea: a case study for mixed action Lattice QCD
• Locality Properties of a New Class of Lattice Dirac Operators
• Lattice formulation of 2D $\mathcal{N}=(2,2)$ SQCD based on the B model twist
• Gauge action improvement and smearing
• Progress using generalized lattice Dirac operators to parametrize the Fixed-Point QCD action
• Dyon structures in the deconfinement phase of lattice gluodynamics: topological clusters, holonomies and Abelian monopoles
• Localized eigenmodes of the overlap operator and their impact on the eigenvalue distribution
• Topological objects in QCD
• Wilson mass dependence of the overlap topological charge density
• On Witten's global anomaly for higher SU(2) representations
• Continuum Limit of Overlap Valence Quarks on a Twisted Mass Sea
• Numerical study of lattice index theorem usingimproved cooling and overlap fermions
• Towards Weyl fermions on the lattice without artefacts
• Perturbative renormalization of the first two moments of non-singlet quark distributions with overlap fermions
• Classical Limits of Scalar and Tensor Gauge Operators Based on the Overlap Dirac Matrix
• More about the axial anomaly on the lattice
• Domain wall fermion and CP symmetry breaking
• Lattice Regularization and Symmetries
• Exact chiral invariance at finite density on the lattice
• Index theorem in spontaneously symmetry-broken gauge theories on a fuzzy 2-sphere
• Ginsparg-Wilson Relation and Lattice Chiral Symmetry in Fermionic Interacting Theories
• Comparing topological charge definitions using topology fixing actions
• Probability of the Standard Model Appearance from a Matrix Model
• Majorana and Majorana-Weyl fermions in lattice gauge theory
• Admissibility Condition and Nontrivial Indices on a Noncommutative Torus
• Machine learning a fixed point action for SU(3) gauge theory with a gauge equivariant convolutional neural network
• Fermion number anomaly with the fluffy mirror fermion
• Lattice QCD with the Overlap Fermions at Strong Gauge Coupling (II)
• CP, T and CPT in the non-perturbative formulation of chiral gauge theories
• Hadron Masses and Quark Condensate from Overlap Fermions
• Vortex fermion on the lattice
• Lorentz symmetry violation in the fermion number anomaly with the chiral overlap operator
• QCD Anderson transition with overlap valence quarks on a twisted-mass sea
• Symmetries of Ginsparg-Wilson Chiral Fermions
• A Perturbative Study of a General Class of Lattice Dirac Operators
• O(a) Improvement of 2D N=(2,2) Lattice SYM Theory
• Improving the Dirac Operator in Lattice QCD
• Partial restoration of chiral symmetry in the color flux tube
• Anomalous gauge theories revisited
• Physics prospects of UV-filtered overlap quarks
• Ultraviolet filtering of lattice configurations and applications to Monte Carlo dynamics
• Machine-learned RG-improved gauge actions and classically perfect gradient flows
• Construction of a topological charge on fuzzy S^2 x S^2 via Ginsparg-Wilson relation
• Renormalisation of one-link quark operators for overlap fermions with Lüscher-Weisz gauge action
• Parity Realization in Lattice QCD with Ginsparg-Wilson Fermions
• Monopole and instanton effects in QCD
• One-loop perturbative coupling of $A$ and $A_{\star }$ through the chiral overlap operator
• Factorization of Fermion Doubles on the Lattice
• Spectra of massive QCD Dirac Operators from Random Matrix Theory: all three chiral symmetry breaking patterns
• Instanton Density Operator in Lattice QCD from Higher Category Theory
• Determinant of a new fermionic action on a lattice - (I)
• Evaluating topological charge density with symmetric multi-probing method
• Ginsparg-Wilson relation on a fuzzy 2-sphere for adjoint matter
• Filtered topological structure of the QCD vacuum: Effects of dynamical quarks
• Wess-Zumino-Witten term on the lattice
• Topological Structure of the QCD Vacuum Revealed by Overlap Fermions
• Lattice Chiral Symmetry in Fermionic Interacting Theories and the Antifield Formalism
• Overlap lattice fermion in a gravitational field
• Four-dimensional lattice chiral gauge theories with anomalous fermion content
• On the chiral anomaly and the Yang-Mills gradient flow
• The locality problem for two tastes of staggered fermions
• Monopoles, spectra of overlap fermions, and eta-prime meson in external magnetic fields
• Topological Obstruction in Block-spin Transformations
• Exact Chiral Invariance at Finite Density on Lattice
• Chern-Simons Type Characteristic Classes of Abelian Lattice Gauge Theory