Received: 31 October 2017 / Revised: 28 December 2017 / Accepted: 12 January 2018 / Published: 29 January 2018

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**Abstract**

Fefferman-Graham ambient construction can be formulated as $\mathfrak{sp}(2)$ -algebra relations on three Hamiltonian constraint functions on ambient space. This formulation admits a simple extension that leads to higher-spin fields, both conformal gauge fields and usual massless fields on anti-de Sitter

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Fefferman-Graham ambient construction can be formulated as $\mathfrak{sp}(2)$ -algebra relations on three Hamiltonian constraint functions on ambient space. This formulation admits a simple extension that leads to higher-spin fields, both conformal gauge fields and usual massless fields on anti-de Sitter spacetime. For the bulk version of the system, we study its possible on-shell version which is formally consistent and reproduces conformal higher-spin fields on the boundary. Interpretation of the proposed on-shell version crucially depends on the choice of the functional class. Although the choice leading to fully interacting higher-spin theory in the bulk is not known, we demonstrate that the system has a vacuum solution describing general higher-spin flat backgrounds. Moreover, we propose a functional class such that the system describes propagation of higher-spin fields over any higher-spin flat background, reproducing all the structures that determine the known nonlinear higher-spin equations.
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(This article belongs to the Special Issue Higher Spin Gauge Theories)