Axial Anomaly and Index of the Overlap Hypercube Operator

Abstract

The overlap hypercube fermion is constructed by inserting a lattice fermion with hypercubic couplings into the overlap formula. One obtains an exact Ginsparg-Wilson fermion, which is more complicated than the standard overlap fermion, but which has improved practical properties and is of current interest for use in numerical simulations. Here we deal with conceptual aspects of the overlap hypercube Dirac operator. Specifically, we evaluate the axial anomaly and the index, demonstrating that the correct classical continuum limit is recovered. Our derivation is non-perturbative and therefore valid in all topological sectors. At the non-perturbative level this result had previously only been shown for the standard overlap Dirac operator with Wilson kernel. The new techniques which we develop to accomplish this are of a general nature and have the potential to be extended to overlap Dirac operators with even more general kernels.

arXiv comment21 pages, no figures, final version to appear in Eur. Phys. J. C

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Cited by in corpus (6)

• Theta dependence of SU(N) gauge theories in the presence of a topological term
• Filtered overlap: speedup, locality, kernel non-normality and Z_A~1
• Overlap Hypercube Fermions in QCD Simulations Near the Chiral Limit
• The index of the overlap Dirac operator on a discretized 2d non-commutative torus
• Optimised Dirac Operators on the Lattice: Construction, Properties and Applications
• Overlap Hypercube Fermions in QCD