Superconformal invariants or how to relate four-point AdS amplitudes

Using the form of N=2$N=2$ superconformal invariants we derive the explicit relation between the bottom and top components of the correlator of four stress-tensor multiplets in N=4$N=4$ super-Yang–Mills. The result is given in terms of an eighth order differential operator acting on the function of two variables which characterises these correlators. It allows us to show a non-trivial consistency relation between the known results for the corresponding supergravity amplitudes on AdS₅${\mathit{AdS}}_5$.