Ultraviolet phenomena in AdS self-interacting quantum field theory

Understand

We study the one-loop corrections to the four-point function in the Anti de Sitter space-time for a $\phi^4$ 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 (non-conformal) 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.