The Absence of Ultralocal Ginsparg-Wilson Fermions

TL;DR

This paper proves that all Ginsparg-Wilson fermions, regardless of the specific form of the relation, cannot be ultralocal but are limited to exponential locality, impacting lattice fermion formulations.

Contribution

It extends Horvath's result by showing that no Ginsparg-Wilson fermions can be ultralocal, only exponentially local, regardless of the form of the relation.

Findings

Ginsparg-Wilson fermions are not ultralocal.

All Ginsparg-Wilson fermions exhibit exponential decay of couplings.

The result applies to all forms of the Ginsparg-Wilson relation.

Abstract

It was shown recently by I. Horvath that lattice fermions obeying the standard form of the Ginsparg-Wilson relation cannot be ultralocal. However, there are more general forms of the Ginsparg-Wilson relation, which also guarantee the physical properties related to chirality, but which are not covered by Horvath's consideration. Here we present a proof which applies to all Ginsparg-Wilson fermions, demonstrating that they can only be local in the sense of an exponential decay of their couplings, but not ultralocal.