Strong Non-Ultralocality of Ginsparg-Wilson Fermionic Actions

TL;DR

This paper proves that constructing a local, hypercubic symmetric Ginsparg-Wilson fermionic action describing single massless fermion species on an infinite lattice is impossible, establishing a fundamental non-ultralocality property.

Contribution

It demonstrates the strong non-ultralocality of Ginsparg-Wilson fermionic actions under broad symmetry and locality conditions, extending previous results on symmetry transformation non-ultralocality.

Findings

Proves the impossibility of ultralocal Ginsparg-Wilson actions with desired properties

Establishes strong non-ultralocality for doubler-free fermionic actions

Complements earlier results on non-ultralocality of symmetry transformations

Abstract

It is shown that it is impossible to construct a free theory of fermions on infinite hypercubic Euclidean lattice in even number of dimensions that: (a) is ultralocal, (b) respects the symmetries of hypercubic lattice, (c) chirally nonsymmetric part of its propagator is local, and (d) describes single species of massless Dirac fermions in the continuum limit. This establishes non-ultralocality for arbitrary doubler-free Ginsparg-Wilson fermionic action with hypercubic symmetries ("strong non-ultralocality"), and complements the earlier general result on non-ultralocality of infinitesimal Ginsparg-Wilson-Luscher symmetry transformations ("weak non-ultralocality").