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

Abstract

The decoupling of heavy fields as required by the Appelquist-Carazzone theorem plays a fundamental role in the construction of any effective field theory. However, it is not a trivial task to implement a renormalization prescription that produces the expected decoupling of massive fields, and it is even more difficult in curved spacetime. Focused on this idea, we consider the renormalization of the one-loop effective action for the Yukawa interaction with a background scalar field in curved space. We compute the beta functions within a generalized DeWitt-Schwinger subtraction procedure and discuss the decoupling in the running of the coupling constants. For the case of a quantized scalar field, all the beta function exhibit decoupling, including also the gravitational ones. For a quantized Dirac field, decoupling appears almost for all the beta functions. We obtain the anomalous result that the mass of the background scalar field does not decouple.

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Cited by in corpus (6)

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• Resummed heat-kernel for surface contributions: Dirichlet semitransparent boundary conditions
• Vacuum Energy and Renormalization of the Field-Independent Term
• Geometry-Induced Vacuum Polarization and Mode Shifts in Maxwell-Klein-Gordon Theory