The Index of a Ginsparg-Wilson Dirac operator

Abstract

A novel feature of a Ginsparg-Wilson lattice Dirac operator is discussed. Unlike the Dirac operator for massless fermions in the continuum, this lattice Dirac operator does not possess topological zero modes for any topologically-nontrivial background gauge fields, even though it is exponentially-local, doublers-free, and reproduces correct axial anomaly for topologically-trivial gauge configurations.

8 pages, minor changes, the version to appear in Phys. Lett. B

References in corpus (1)

• Perturbation Calculation of the Axial Anomaly of a Ginsparg-Wilson lattice Dirac operator

Cited by in corpus (13)

• The U_A(1) Problem on the Lattice with Ginsparg-Wilson Fermions
• Accelerated Overlap Fermions
• More chiral operators on the lattice
• Quenched chiral logarithms in lattice QCD with exact chiral symmetry
• Perturbation Calculation of the Axial Anomaly of a Ginsparg-Wilson lattice Dirac operator
• Axial Anomaly and Index of the Overlap Hypercube Operator
• A renormalisation group derivation of the overlap formulation
• Optimised Dirac Operators on the Lattice: Construction, Properties and Applications
• Form and index of Ginsparg-Wilson fermions
• Beauty mesons in $N_f=2+1+1+1$ lattice QCD with exact chiral symmetry
• Chiral fermion operators on the lattice
• The Index and Axial Anomaly of a lattice Dirac operator
• Naive Lattice Fermion without Doublers