  It is shown that a nonlinear derivative-dependent transformation of gravity
fields changes correlation functions in a boundary CFT, and, therefore,
corresponds to a change of a basis of operators in the CFT. It is argued that
only non-renormalized structures in correlation functions can be changed by
such a field transformation, and that the study of the response of correlation
functions to gravity field transformations allows one to find them. In the case
of 4-point functions of CPOs in SYM_4 several non-renormalized structures are
found, including the extremal and subextremal ones. It is also checked that
quartic couplings of scalar fields s^I that are dual to extended chiral primary
operators vanish in the subextremal case, as dictated by the
non-renormalization theorem for the subextremal 4-point functions and the
AdS/CFT correspondence.
