On the correspondence between gravity fields and CFT operators

It is shown that a non-linear derivative-dependent transformation of gravit y fields changes correlation functions in a boundary CFT, and, therefore, c orresponds to a change of a basis of operators in the CFT. It is argued tha t only non-renormalized structures in correlation functions can be changed by such a field transformation, and that the study of the response of corre lation functions to gravity field transformations allows one to find them. In the case of 4-point functions of CPOs in SYM4 several non-renormalized s tructures are found, including the extremal and subextremal ones. It is als o checked that quartic couplings of scalar fields s(I) that are dual to ext ended chiral primary operators vanish in the subextremal case, as dictated by the non-renormalization theorem for the subextremal 4-point functions an d the AdS/CFT correspondence.