On the Absence of Ultralocal Ginsparg-Wilson Fermions

It was shown recently by I. Horváth 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 chiral properties, but which are not covered by Horváth’s consideration. Here we extend his proof to a much larger class of Ginsparg-Wilson fermions, demonstrating that they can only be local in the sense of an exponential decay of their couplings, but not ultralocal.