Continuum limit of the axial anomaly and index for the staggered overlap Dirac operator: An overview

TL;DR

This paper investigates how the axial anomaly and index behave in the continuum limit for the staggered overlap Dirac operator, highlighting unique complications and the necessity of averaging over hypercube sites.

Contribution

It provides an overview of the continuum limit behavior of the axial anomaly and index for the staggered overlap Dirac operator, addressing new complications in the formalism.

Findings

The index correctly reproduces the continuum index.

The axial anomaly requires averaging over hypercube sites to match the continuum.

New complications arise due to spin and flavor distribution in the staggered formalism.

Abstract

Evaluation of the continuum limit of the axial anomaly and index is sketched for the staggered overlap Dirac operator. There are new complications compared to the usual overlap case due to the distribution of the spin and flavor components around lattice hypercubes in the staggered formalism. The index is found to correctly reproduce the continuum index, but for the axial anomaly this is only true after averaging over the sites of a lattice hypercube.