Abstract
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.
Highlights
The theory of higher-spin gravity is intimately tied to Anti de Sitter/Conformal Field theory (AdS/CFT) correspondence [1,2,3] in the exotic regime of strong curvature/weak coupling [4,5,6]
The discovery of the deep relationship between AdS massless fields and elementary fields living on the conformal boundary by Flato and Fronsdal [7] anticipated some ideas of AdS/CFT correspondence
Particular examples where the connection between both subjects might deserve to be explored further are the ambient construction of Fefferman and Graham and its relation to effective actions and higher-spin gauge fields that we investigate in this work
Summary
The theory of higher-spin gravity is intimately tied to Anti de Sitter/Conformal Field theory (AdS/CFT) correspondence [1,2,3] in the exotic regime of strong curvature/weak coupling [4,5,6]. It is not clear how to extend this beyond the free approximation: a natural suggestion to put the system on-shell at higher orders is to introduce extra gauge symmetry factoring out the ideal generated by the sp(2)-fields themselves This extra gauge symmetry is precisely the one needed to describe CHS fields on the boundary and can be seen as a natural gauge symmetry of the constrained system with constraints Fi , which is related to a redefinition of the constraints
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