Low energy effective action of domain-wall fermion and the Ginsparg-Wilson relation

Abstract

We derive the effective action of the light fermion field of the domain-wall fermion, which is referred as $q(x)$ by Furman and Shamir. The inverse of the effective Dirac operator turns out to be identical to the inverse of the truncated overlap Dirac operator, except a local contact term which would give the chiral symmetry breaking in the Ginsparg-Wilson relation. This result allows us to relate the light fermion field and the fermion field described by the truncated overlap Dirac operator and to understand the chiral property of the light fermion through the exact chiral symmetry based on the Ginsparg-Wilson relation.

35 pages, LaTeX2e, references added and updated, minor corrections

References in corpus (7)

• Exact chiral symmetry on the lattice and the Ginsparg-Wilson relation
• More about exactly massless quarks on the lattice
• Locality properties of Neuberger's lattice Dirac operator
• Anomalous Chiral Symmetry Breaking above the QCD Phase Transition
• On the Neuberger overlap operator
• GW fermion propagators and chiral condensate
• Light quark masses using domain wall fermions

Cited by in corpus (23)

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• An Introduction to Chiral Symmetry on the Lattice
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• Violation of chirality of the Möbius domain-wall Dirac operator from the eigenmodes
• On the decoupling of mirror fermions
• Möbius domain-wall fermions on gradient-flowed dynamical HISQ ensembles
• A Chiral Solution to the Ginsparg-Wilson Equation
• Lattice QCD at the end of 2003
• Schroedinger functional formalism with Ginsparg-Wilson fermion
• Hierarchically deflated conjugate gradient
• Solving the local cohomology problem in U(1) chiral gauge theories within a finite lattice
• Multigrid for Chiral Lattice Fermions: Domain Wall
• Schroedinger functional formalism with domain-wall fermion
• A simple construction of fermion measure term in U(1) chiral lattice gauge theories with exact gauge invariance
• Probing the chiral weak Hamiltonian at finite volumes
• Spectral properties and chiral symmetry violations of (staggered) domain wall fermions in the Schwinger model
• Determination of the $\Delta S=1$ weak Hamiltonian in the SU(4) chiral limit through topological zero-mode wave functions
• A formulation of domain-wall fermions in the Schrödinger functional
• Topics in Lattice QCD and Effective Field Theory
• Chiral symmetry on the lattice
• CP symmetry and lattice chiral gauge theories
• A note on ultraviolet suppressed quasi-optimal domain wall fermions