  We study four-point correlation functions of 1/2-BPS operators in N=4 SYM
which are dual to massive KK modes in AdS_5 supergravity. On the field theory
side, the procedure of inserting the SYM action yields partial
non-renormalisation of the four-point amplitude for such operators. In
particular, if the BPS operators have dimensions equal to three or four, the
corresponding four-point amplitude is determined by one or two independent
functions of the two conformal cross-ratios, respectively. This restriction on
the amplitude does not merely follow from the superconformal Ward identities,
it also encodes dynamical information related to the structure of the gauge
theory Lagrangian. The dimension 3 BPS operator is the AdS/CFT dual of the
first non-trivial massive Kaluza-Klein mode of the compactified type IIB
supergravity, whose interactions go beyond the level of the five-dimensional
gauged N=8 supergravity. We show that the corresponding effective Lagrangian
has a surprisingly simple sigma-model-type form with at most two derivatives.
We then compute the supergravity-induced four-point amplitude for the dimension
3 operators. Remarkably, this amplitude splits into a "free" and an
"interacting" parts in exact agreement with the structure predicted by the
insertion procedure. The underlying OPE fulfills the requirements of
superconformal symmetry and unitarity.
