Renormalization group and decoupling in curved space

Abstract

I outline a series of results obtained in collaboration with I.L. Shapiro. The renormalization group equations and decoupling of massive fields in curved spacetime are studied and the cases of massive scalar, fermion, and vector fields are considered. In the higher derivative sector we arrive at the standard form of decoupling and obtain the renormalization group β-functions in both UV and IR regimes as the limits of general expressions. For the cosmological and Newton constants the corresponding β-functions turned out to be unaccessible in the perturbative regime and, in particular, the form of decoupling remains unclear.