Axial Anomaly and Index of the Overlap Hypercube Operator

TL;DR

This paper analyzes the axial anomaly and index of the overlap hypercube fermion, demonstrating that it correctly reproduces the continuum limit non-perturbatively, with potential for broader kernel applications.

Contribution

It provides a non-perturbative evaluation of the axial anomaly and index for the overlap hypercube operator, extending previous results to more general kernels.

Findings

Correct continuum limit of the axial anomaly demonstrated

Non-perturbative proof valid in all topological sectors

Development of general techniques for overlap operators

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.