On the zero of the fermion zero mode

TL;DR

This paper proves that fermionic zero modes in non-trivial gauge backgrounds must have zeros, linking their location to monopoles and suggesting a method to identify topological features in lattice simulations.

Contribution

It provides a topological proof that fermionic zero modes must have zeros in non-trivial gauge backgrounds, applicable to various configurations including calorons.

Findings

Fermionic zero modes must have zeros in non-trivial backgrounds.

The zero's location relates to constituent monopoles in calorons.

Proposes using zero modes to detect topological content in lattice simulations.

Abstract

We argue that the fermionic zero mode in non-trivial gauge field backgrounds must have a zero. We demonstrate this explicitly for calorons where its location is related to a constituent monopole. Furthermore a topological reasoning for the existence of the zero is given which therefore will be present for any non-trivial configuration. We propose the use of this property in particular for lattice simulations in order to uncover the topological content of a configuration.