A comment on the Nielsen-Ninomiya theorem

An example of a local lattice hamiltonian in three space dimensions whose continuum limit spectrum consists of a single free Weyl particle and a set of non-propagating modes is presented. Our model satisfies all the hypotheses of the Nielsen-Ninomiya theorem. However, when locally coupled to a background abelian gauge field, it fails to exhibit the spectrum and anomalies expected for a charged Weyl field.