Higher Spin Extension of Fefferman-Graham Construction

TL;DR

This paper extends the Fefferman-Graham construction to include higher-spin fields, providing a formal framework that reproduces known higher-spin equations and describes propagation over higher-spin backgrounds.

Contribution

It introduces a higher-spin extension of the Fefferman-Graham construction using $rak{sp}(2)$-algebra relations, and explores its on-shell version and background solutions.

Findings

System admits a vacuum solution with higher-spin flat backgrounds

Proposes a functional class for higher-spin propagation over backgrounds

Reproduces structures of known nonlinear higher-spin equations

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 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.