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The decoupling of heavy fields as required by the Appelquist-Carazzonetheorem plays a fundamental role in the construction of any effective fieldtheory. However, it is not a trivial task to implement a renormalizationprescription that produces the expected decoupling of massive fields, and it iseven more difficult in curved spacetime. Focused on this idea, we consider therenormalization of the one-loop effective action for the Yukawa interactionwith a background scalar field in curved space. We compute the beta functionswithin a generalized DeWitt-Schwinger subtraction procedure and discuss thedecoupling in the running of the coupling constants. For the case of aquantized scalar field, all the beta function exhibit decoupling, includingalso the gravitational ones. For a quantized Dirac field, decoupling appearsalmost for all the beta functions. We obtain the anomalous result that the massof the background scalar field does not decouple.

Renormalization, running couplings and decoupling for the Yukawa model in curved spacetime