Decoupling a fermion whose mass comes from a Yukawa coupling: Nonperturbative considerations

Perturbative analyses seem to suggest that fermions whose mass comes solely from a Yukawa coupling to a scalar field can be made arbitrarily heavy, while the scalar remains light. The effects of the fermion can be summarized by a local effective Lagrangian for the light degrees of freedom. Using weak coupling and large-N techniques, we present a variety of models in which this conclusion is shown to be false when nonperturbative variations of the scalar field are considered. The heavy fermions contribute nonlocal terms to the effective action for light degrees of freedom. This resolves paradoxes about anomalous and nonanomalous symmetry violation in these models. The application of these results to lattice gauge theory implies that attempts to decouple lattice fermion doublers by the method of Swift and Smit cannot succeed, a result already suggested by lattice calculations