Nonperturbative decoupling and effective field theory.

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We examine recent claims that nonperturbative effects can prevent the decoupling of a heavy fermion whose mass arises from a Yukawa coupling to a scalar field. We show that in weakly coupled, four-dimensional models such as the standard model with heavy mirror fermions the effects of the heavy fermions can always be accounted for by local operators involving light fields. We contrast this with the case of the (1+1)-dimensional Abelian Higgs model, in which there does not appear to be a local effective field theory describing the low energy physics when heavy fermions are integrated out.