AdS_4/CFT_3 Construction from Collective Fields

TL;DR

This paper develops a precise method to reconstruct AdS_4 space-time and higher-spin fields from a three-dimensional O(N) vector model using collective fields, establishing a direct bulk-boundary correspondence.

Contribution

It introduces an exact null plane quantization map linking CFT_3 collective fields to AdS_4 higher-spin theory, enabling explicit bulk reconstruction.

Findings

Exact AdS_4 space-time reconstruction from CFT_3 collective fields

Map between bi-local collective coordinates and AdS_4 geometry

Explicit realization of higher-spin fields in AdS_4 from boundary data

Abstract

We pursue the construction of higher-spin theory in AdS_4 from CFT_3 of the O(N) vector model in terms of canonical collective fields. In null plane quantization an exact map is established between the two spaces. The coordinates of the AdS_4 space-time are generated from the collective coordinates of the bi-local field. This, in the light cone gauge, provides an exact one to one reconstruction of bulk AdS_4 space-time and higher-spin fields.