Ginsparg-Wilson-Lüscher symmetry and ultralocality

Abstract

Important recent discoveries suggest that Ginsparg-Wilson-L\"uscher (GWL) symmetry has analogous dynamical consequences for the theory on the lattice as chiral symmetry does in the continuum. While it is well known that an inherent property of lattice chiral symmetry is fermion doubling, we show here that an inherent property of GWL symmetry is that the infinitesimal symmetry transformation couples fermionic degrees of freedom at arbitrarily large lattice distances (non-ultralocality). The consequences of this result for the ultralocality of symmetric actions are discussed.