Exact chiral symmetry on the lattice and the Ginsparg-Wilson relation

Abstract

It is shown that the Ginsparg-Wilson relation implies an exact symmetry of the fermion action, which may be regarded as a lattice form of an infinitesimal chiral rotation. Using this result it is straightforward to construct lattice Yukawa models with unbroken flavour and chiral symmetries and no doubling of the fermion spectrum. A contradiction with the Nielsen-Ninomiya theorem is avoided, because the chiral symmetry is realized in a different way than has been assumed when proving the theorem.

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References in corpus (2)

• The index theorem in QCD with a finite cut-off
• Lattice QCD without tuning, mixing and current renormalization

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• Streda formula for the Hofstadter-Wilson-Dirac model in two and four dimensions
• Dominance of a single topological sector in gauge theory on non-commutative geometry
• A generalized Ginsparg-Wilson relation
• Chiral property of domain-wall fermion from eigenvalues of 4D Wilson-Dirac Operator
• Instanton Density Operator in Lattice QCD from Higher Category Theory
• Probability distribution over some phenomenological models in the matrix model compactified on a torus
• Anomalies and symmetries of the regularized action
• Exploring the role of the charm quark in the $\Delta I=1/2$ rule
• The Ultraviolet Structure of Quantum Field Theories. Part 2: What is Quantum Field Theory?
• On-shell and off-shell improvement for Ginsparg-Wilson fermions
• Ginsparg-Wilson relation on a fuzzy 2-sphere for adjoint matter
• Two-loop Wess-Zumino model with exact supersymmetry on the lattice
• Wess-Zumino-Witten term on the lattice
• Matrix Model and Ginsparg-Wilson Relation
• Spectrum of the fixed point Dirac operator in the Schwinger model
• On the Isomorphic Description of Chiral Symmetry Breaking by Non-Unitary Lie Groups
• Exact Ward-Takahashi identity for the lattice N=1 Wess-Zumino model
• Dynamical overlap fermions with increased topological tunnelling
• Multigrid Preconditioning for the Overlap Operator in Lattice QCD
• Chiral violations in domain-wall QCD from one-loop perturbation theory at finite $N_s$
• A lattice Dirac operator for QCD with light dynamical quarks
• Massive Overlap Fermions on Anisotropic Lattices
• Overlap Hypercube Fermions in QCD
• Chiral symmetry restoration and axial vector renormalization for Wilson fermions
• On the infinite gradient-flow for the domain-wall formulation of chiral lattice gauge theories
• Chiral fermion operators on the lattice
• Feasibility study of using the overlap-Dirac operator for hadron spectroscopy
• Exact results and approximation schemes for the Schwinger model with the overlap Dirac operator
• Dirac zero-modes in compact U(1) gauge theory
• Lattice renormalisation of O(a) improved heavy-light operators
• Topological susceptibility for the SU(3) Yang--Mills theory
• Test of the Schrödinger functional with chiral fermions in the Gross-Neveu model
• Another approach to local cohomology problem in abelian lattice gauge theories
• Lattice chiral symmetry, CP-violation and Majorana fermions
• Chiral symmetry breaking from Ginsparg-Wilson fermions
• Remarks on left-handed lattice fermions
• Phase structures of strong coupling lattice QCD with overlap fermions at finite temperature and chemical potential
• Multi-grid HMC for Ginsparg-Wilson fermions
• Topological Structure of the QCD Vacuum Revealed by Overlap Fermions
• Block renormalization group transformations and overlap fermions
• Axial anomaly and Ginsparg-Wilson fermions in the Lattice Dirac Sea picture
• The eigSUMR inverter for overlap fermion
• Spectrum of the Hermitian Wilson-Dirac Operator for a Uniform Magnetic Field in Two Dimensions
• Lattice Chiral Symmetry in Fermionic Interacting Theories and the Antifield Formalism
• Overlap lattice fermion in a gravitational field
• Chiral symmetry on the lattice
• Minimal-doubling and single-Weyl Hamiltonians
• Pythagoras' Theorem on a 2D-Lattice from a "Natural" Dirac Operator and Connes' Distance Formula
• Domain-wall fermions and chiral symmetries
• Anomaly of conserved and nonconserved axial charges in Hamiltonian lattice gauge theory
• Generalized Ginsparg-Wilson algebra and index theorem on the lattice
• Quenched QCD at finite temperature with overlap Fermions
• Understanding the index theorems with massive fermions
• Anomalous Lorentz and CPT violation
• A confederacy of anomalies
• Unquenched domain wall quarks with multi-bosons
• Fermion Discretization Effects in the Two-Flavor Lattice Schwinger Model: A Study with Matrix Product States
• B_K from quenched overlap QCD
• On the chiral anomaly and the Yang-Mills gradient flow
• Chiral symmetry on a lattice with hopping interactions
• Random Matrix Theory and the Spectra of Overlap Fermions
• Axial anomaly in the reduced model: Higher representations
• Overlap Dirac operator with chiral chemical potential and Chiral Magnetic Effect on the lattice
• Hadron Structure on the Lattice
• Regularisation of Chiral Gauge Theories
• Low Energy Constants from the zero mode contribution to the pseudo-scalar correlator
• Supercurrent conservation in the lattice Wess-Zumino model with Ginsparg-Wilson fermions
• Exploring the Nucleon Structure from First Principles of QCD
• Spontaneous chiral symmetry breaking on the lattice
• Lattice supersymmetry and string phenomenology
• Low-lying Dirac eigenmodes and monopoles in 4D compact QED
• Four-dimensional lattice chiral gauge theories with anomalous fermion content
• Simulating chiral quarks in the epsilon-regime of QCD
• Lattice QED and Universality of the Axial Anomaly
• Overlap Fermion in External Gravity
• Dirac operator normality and chiral properties
• A Ginsparg-Wilson approach to lattice $\mathcal{C}\mathcal{P}$ symmetry
• Exact Chiral Invariance at Finite Density on Lattice
• Reflection Positivity of Free Overlap Fermions
• Criterium for the index theorem on the lattice
• Monopoles, spectra of overlap fermions, and eta-prime meson in external magnetic fields
• Chiral symmetry restoration and eigenvalue density of Dirac operator
• A Note on Reflection Positivity and the Umezawa-Kamefuchi-Kallen-Lehmann Representation of Two Point Correlation Functions
• The conserved axial current in the presence of multiple chiral symmetries
• From spin models to lattice QCD -- the scientific legacy of Peter Hasenfratz
• Symmetry and Symmetry Restoration of Lattice Chiral Fermion in the Overlap Formalism
• Topological Obstruction in Block-spin Transformations
• High precision applications of lattice gauge theories in the quest for new physics
• More chiral lattice fermions
• Lattice measurement of $B_{B_s}$ with a chiral light quark action
• CP and T violation in non-perturbative chiral gauge theories
• Construction of lattice Möbius domain wall fermions in the Schrödinger functional scheme
• Chiral symmetry in lattice QCD
• Monopole and instanton effects on connected and disconnected correlations for scalar density
• Lattice fermion formulation via Physics-Informed Neural Networks: Ginsparg-Wilson relation and Overlap fermions
• Estimating ${\chi }_{\mathrm{top}}$ Lattice Artifacts from Flowed SU(2) Calorons
• Dynamical fermions in lattice quantum chromodynamics
• PQChPT with Staggered Sea and Valence Ginsparg-Wilson Quarks: Vector Meson Masses
• Low-lying Dirac eigenmodes and monopoles in 3+1D compact QED
• Probing QCD instantons using jet correlation observables in proton-proton collisions at the LHC
• A further extension to the group of Ginsparg-Wilson (overlap) chiral symmetries
• New One-Flavor Hybrid Monte Carlo Simulation Method for Lattice Fermions with gamma-five Hermiticity
• Improved Overlap Fermions
• Accelerating iterative linear equation solver using modified domain-wall fermion matrix in lattice QCD simulations
• O(a^2) improvement of the overlap-Dirac operator