Collective Dipole Model of AdS/CFT and Higher Spin Gravity

TL;DR

The paper presents a first-quantized, world-sheet–like construction of AdS/CFT for the O(N) vector model using a bilocal collective dipole composed of two Minkowski particles. Through a careful gauge fixing and a canonical transformation, the dipole is shown to reproduce the AdS_{d+1} spacetime together with the infinite tower of higher-spin fields, generalizing previous AdS_4 results to arbitrary dimensions via an explicit dipole–bulk map. The core result is a one-to-one canonical transformation that maps the dipole phase space to the AdS higher-spin particle phase space, thereby realizing the Flato–Fronsdal tensor-product structure in any dimension. This provides a transparent, first-quantized mechanism for emergent bulk geometry and higher-spin degrees of freedom from a boundary CFT, with potential avenues toward BRST quantization and deeper insights into locality in AdS.

Abstract

We formulate a first quantized construction of the AdS_{d+1}/CFT_d correspondence using the bi-local representation of the free d-dimensional large N vector model. The earlier reconstruction of AdS_4 higher-spin gravity provides a scheme where the AdS spacetime (and higher-spin fields) are given by the composite bi-local fields. The underlying first quantized, world-sheet picture is extracted in the present work and generalized to any dimension. A higher-spin AdS particle model is shown to emerge from the collective bi-particle system of Minkowski particles through a canonical transformation. As such this construction provides a simple explicit mechanism of the AdS/CFT correspondence.