Towards higher-spin holography in ambient space of any dimension

TL;DR

Addresses constructing explicit boundary-to-bulk propagators for bosonic higher-spin fields in $AdS_{d+1}$ across dimensions. Develops an algebraic, differential-equation-free method based on ambient-space geometry, unfolding, and star-products to produce a generating function for the spin-$s$ Weyl tensor and an integral map that determines the full $B$-propagator from the master connection data. Derives $W$- and $B$-propagators for all spins, connecting them to boundary two-point functions of conserved currents and detailing the boundary-to-bulk map. This approach facilitates AdS/CFT tests for higher-spin theories in arbitrary dimensions and provides a practical route to correlation-function calculations in vector-model duals. It clarifies how CKTs and conformal representation theory underpin the coupling of HS fields to boundary operators.

Abstract

We derive the propagators for higher-spin master fields in anti-de Sitter space of arbitrary dimension. A method is developed to construct the propagators directly without solving any differential equations. The use of the ambient space, where AdS is represented as a hyperboloid and its conformal boundary as a projective light-cone, simplifies the approach and makes a direct contact between boundary-to-bulk propagators and two-point functions of conserved currents.