Constraints on the existence of chiral fermions in interacting lattice theories

Abstract

Any interacting theory defined on a regular lattice is shown to have a vector-like spectrum if the following conditions are satisfied: (a) hermiticity, (b) locality, (c) relativistic continuum limit without massless bosons, and (d) pole-free effective vertex functions for conserved currents. The proof exploits the zero frequency inverse retarded propagator of an appropriate set of interpolating fields as an effective quadratic hamiltonian, to which the Nielsen-Ninomiya theorem is applied.