Exact local fermionic zero modes

TL;DR

This paper presents a straightforward method to identify localized exact fermionic zero modes associated with specific gauge configurations across various lattice gauge theories, revealing a finite density of near-zero modes in quenched four-dimensional simulations.

Contribution

It introduces a simple, general approach to find localized fermionic zero modes for any local fermionic action, applicable to multiple lattice gauge theories and configurations.

Findings

Finite density of almost zero modes in quenched 4D lattice gauge theory.

Exponential suppression of zero mode density with increasing gauge coupling.

Applicability to staggered and Wilson fermions in multiple dimensions.

Abstract

We introduce a simple method to find localized exact fermionic zero modes for any local fermionic action. The zero modes are attached to specific local gauge configurations. Examples are provided for staggered and Wilson fermion actions in 2-6 dimensions, at finite and infinite lattice volumes, and for abelian and non-abelian gauge groups. One of our concrete results is that a finite density of almost zero modes must occur in quenched four dimensional lattice gauge theory simulations that use traditional methods. This density is exponentially suppressed in the gauge coupling constant.