Ultraviolet phenomena in AdS self-interacting quantum field theory

We study the one-loop corrections to the four-point function in the Anti de Sitter space-time for a ϕ4 field theory. Our calculation shows the existence of non-local counterterms which however respect the AdS isometry. Our arguments are quite general and applicable to other AdS field theories. We also explain why calculations in Euclidean and Lorentzian signatures should differ even at the leading order in non globaly hyperbolic manifolds.