Tests of the lattice index theorem

TL;DR

This paper examines the lattice index theorem and zero-mode localization in thick classical center vortices, revealing discrepancies in the index for non-orientable spherical vortices despite near-trivial plaquettes.

Contribution

It provides new insights into the behavior of the overlap Dirac operator and topological charge in non-orientable vortex configurations on the lattice.

Findings

Index differs from topological charge in non-orientable vortices

Plaquette traces deviate minimally from trivial values

Links are close to non-trivial center elements in Landau gauge

Abstract

We investigate the lattice index theorem and the localization of the zero-modes for thick classical center vortices. For non-orientable spherical vortices, the index of the overlap Dirac operator differs from the topological charge although the traces of the plaquettes deviate only by a maximum of 1.5% from trivial plaquettes. This may be related to the fact that even in Landau gauge some links of these configuration are close to the non-trivial center elements.