On the correspondence between gravity fields and CFT operators

TL;DR

This work analyzes how nonlinear derivative-dependent gravity field redefinitions in the AdS/CFT framework modify boundary CFT correlators, interpreting these changes as a reshaping of the operator basis. It shows that such redefinitions affect only non-renormalized structures, and through explicit boundary-term analysis of 3- and 4-point functions of extended CPOs, it demonstrates possible mappings to the correlators of single-trace CPOs for extremal and subextremal configurations. The study reinforces that scalars $s^I$ dual to extended CPOs arise naturally from KK reduction and that a complete equivalence to single-trace correlators would require broader field redefinitions beyond scalars. Overall, the results illuminate how operator bases and non-renormalization theorems govern the AdS/CFT dictionary for multi-trace admixtures and provide a framework for testing the duality via protected correlators.

Abstract

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.