AdS Maps and Diagrams of Bi-local Holography

TL;DR

This paper details a bi-local holography framework that reconstructs AdS bulk theories from boundary data, explicitly mapping to higher spin fields and generating bulk diagrams through collective actions.

Contribution

It introduces a constructive scheme for bi-local holography, providing explicit mappings and interaction specifications for AdS and higher spin theories.

Findings

Explicit double Fourier transform mapping to AdS and higher spin fields

Generation of bulk Feynman (Witten) diagrams at tree and loop levels

Detailed evaluation of four-point interactions

Abstract

We present in detail the basic ingredients contained in bi-local holography, representing a constructive scheme for reconstructing AdS bulk theories in Vectorial/AdS duality. Explicit Mapping to bulk AdS and higher spin fields is seen to be given by a double Fourier transform. All order interactions are explicitly specified through the collective action. This generates bulk Feynman (Witten) diagrams (at tree and loop level). We give details of the four-point case evaluation. It is noted that the bi-local construction goes beyond the assumptions in various discussions of non-locality.