Arbitrary-spin effective potentials in anti-de Sitter spacetime

The one-loop effective potentials and stress-energy tensors for fields of arbitrary spin in anti-de Sitter (AdS) spacetime are calculated using the ζ-function technique. The arbitrary-spin ζ function is computed exactly on the four-dimensional hyperbolic space H4, which is the (noncompact) Euclidean section appropriate to AdS spacetime. The finite parts of the effective potentials are given explicitly in terms of integrals containing ψ functions. Applications to AdS supergravity are pointed out.