Higher Spin Extension of Fefferman-Graham Construction

• Main Authors: Xavier Bekaert, Maxim Grigoriev, Evgeny Skvortsov
• Format: Article
• Language: English
• Published: MDPI AG 2018-01-01
• Series: Universe
• Subjects: higher-spin theory; AdS/CFT; Fefferman-Graham
• Online Access: http://www.mdpi.com/2218-1997/4/2/17

Fefferman-Graham ambient construction can be formulated as 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.