On the correspondence between gravity fields and CFT operators

TL;DR

This paper explores how nonlinear transformations of gravity fields affect boundary CFT correlation functions, revealing non-renormalized structures and confirming vanishing couplings consistent with non-renormalization theorems.

Contribution

It demonstrates that certain gravity field transformations correspond to basis changes in CFT operators and identifies non-renormalized correlation structures in SYM_4.

Findings

Non-renormalized structures in 4-point functions identified

Quartic couplings vanish in subextremal cases

Transformation effects linked to operator basis changes

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.