Axial anomaly and topological charge in lattice gauge theory with Overlap Dirac operator

Abstract

An explicit, detailed evaluation of the classical continuum limit of the axial anomaly/index density of the overlap Dirac operator is carried out in the infinite volume setting, and in a certain finite volume setting where the continuum limit involves an infinite volume limit. Our approach is based on a novel power series expansion of the overlap Dirac operator. The correct continuum expression is reproduced when the parameter $m_0$ is in the physical region $0<m_0<2$. This is established for a broad range of continuum gauge fields. An analogous result for the fermionic topological charge, given by the index of the overlap Dirac operator, is then established for a class of topologically non-trivial fields in the aforementioned finite volume setting. Problematic issues concerning the index in the infinite volume setting are also discussed.

Latex, 33 pages. v6: shortened and (hopefully) more succinct version, to appear in Ann.Phys

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Cited by in corpus (53)

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• Microscopic Origin of \boldmath{$U_A(1)$} Symmetry Violation in the High Temperature Phase of QCD
• Quark spins and Anomalous Ward Identity
• A Lattice Study of Quark and Glue Momenta and Angular Momenta in the Nucleon
• Chiral Lattice Gauge Theories Via Mirror-Fermion Decoupling: A Mission (im)Possible?
• The Parton Orbital Angular Momentum: Status and Prospects
• Index Theorem and Overlap Formalism with Naive and Minimally Doubled Fermions
• Topology and higher dimensional representations
• Strange and Charm Quark Spins from Anomalous Ward Identity
• Overlap Hypercube Fermions in QCD Simulations Near the Chiral Limit
• Axial anomaly with the overlap-Dirac operator in arbitrary dimensions
• Supersymmetry, chiral symmetry and the generalized BRS transformation in lattice formulations of 4D $\mathcal{N}=1$ SYM
• A Chiral Solution to the Ginsparg-Wilson Equation
• Gauge Field Strength Tensor from the Overlap Dirac Operator
• The index of the overlap Dirac operator on a discretized 2d non-commutative torus
• The rooting issue for a lattice fermion formulation similar to staggered fermions but without taste mixing
• On the gauge invariant path-integral measure for the overlap Weyl fermions in $\underline{16}$ of SO(10)
• Lattice chirality and the decoupling of mirror fermions
• Why is the mission impossible? -- Decoupling the mirror Ginsparg-Wilson fermions in the lattice models for two-dimensional abelian chiral gauge theories
• SU(2) Gluodynamics and HP1 sigma-model embedding: Scaling, Topology and Confinement
• Wilson mass dependence of the overlap topological charge density
• Solving the local cohomology problem in U(1) chiral gauge theories within a finite lattice
• Atiyah-Patodi-Singer index on a lattice
• More about the axial anomaly on the lattice
• A simple construction of fermion measure term in U(1) chiral lattice gauge theories with exact gauge invariance
• Classical Limits of Scalar and Tensor Gauge Operators Based on the Overlap Dirac Matrix
• Domain wall fermion and CP symmetry breaking
• Confining string and its widening in HP1 embedding approach
• Quark masses, the Dashen phase, and gauge field topology
• General bounds on the Wilson-Dirac operator
• Axial Anomaly and Index of the Overlap Hypercube Operator
• A construction of the Glashow-Weinberg-Salam model on the lattice with exact gauge invariance
• Fermion number anomaly with the fluffy mirror fermion
• Optimised Dirac Operators on the Lattice: Construction, Properties and Applications
• A renormalisation group derivation of the overlap formulation
• A numerical solution to the local cohomology problem in U(1) chiral gauge theories
• Lattice Gauge Fields Topology Uncovered by Quaternionic sigma-model Embedding
• Lorentz symmetry violation in the fermion number anomaly with the chiral overlap operator
• Lattice chirality, anomaly matching, and more on the (non)decoupling of mirror fermions
• Chiral fermion in the Hamiltonian lattice gauge theory
• New solutions to the Ginsparg-Wilson equation
• Parity Realization in Lattice QCD with Ginsparg-Wilson Fermions
• Canonical Approach to Ginsparg-Wilson Fermion
• Streda formula for the Hofstadter-Wilson-Dirac model in two and four dimensions
• Axial anomaly in the reduced model: Higher representations
• Lattice QCD and the Neutron Electric Dipole Moment
• Wess-Zumino-Witten term on the lattice
• Overlap Hypercube Fermions in QCD
• $K$-theoretic computation of the Atiyah(-Patodi)-Singer index of lattice Dirac operators
• Overlap lattice fermion in a gravitational field
• Anomaly of conserved and nonconserved axial charges in Hamiltonian lattice gauge theory
• New term in effective field theory at fixed topology
• Index theorem with Minimally Doubled Fermions in four space-time dimensions