Abstract
It is shown that an interacting theory, defined on a regular lattice, must have a vectorlike spectrum if the following conditions are satisfied: (a) locality, (b) relativistic continuum limit without massless bosons, and (c) 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.
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