A comment on the dual field in the AdS-CFT correspondence

TL;DR

This paper analyzes the duality in the perturbative AdS-CFT correspondence, focusing on how boundary values and bulk field limits relate through functional integrals and Feynman/Witten graphs.

Contribution

It clarifies the manifestation of duality in AdS-CFT by examining the structure of functional integrals and the relationship between boundary and bulk fields.

Findings

Witten graphs are boundary limits of Feynman graphs.

Dual conformal correlation functions are limits of bulk correlation functions.

The duality manifests through the structure of functional integrals.

Abstract

In the perturbative AdS-CFT correspondence, the dual field whose source are the prescribed boundary values of a bulk field in the functional integral, and the boundary limit of the quantized bulk field are the same thing. This statement is due to the fact that Witten graphs are boundary limits of the corresponding Feynman graphs for the bulk fields, and hence the dual conformal correlation functions are limits of bulk correlation functions. This manifestation of duality is analyzed in terms of the underlying functional integrals of different structure.