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Using ambient space we develop a fully gauge and o(d,2) covariant approach toboundary values of AdS(d+1) gauge fields. It is applied to the study of(partially) massless fields in the bulk and (higher-order) conformal scalars,i.e. singletons, as well as (higher-depth) conformal gauge fields on theboundary. In particular, we identify the corresponding Fradkin-Tseytlinequations as obstructions to the extension of the off-shell boundary value tothe bulk, generalizing the usual considerations for the holographic anomaliesto the partially massless fields. We also relate the background fields for thehigher-order singleton to the boundary values of partially massless fields andprove the appropriate generalization of the Flato-Fronsdal theorem, which is inagreement with the known structure of symmetries for the higher-order waveoperator. All these facts support the following generalization of thehigher-spin holographic duality: the O(N) model at a multicritical isotropicLifshitz point should be dual to the theory of partially massless symmetrictensor fields described by the Vasiliev equations based on the higher-ordersingleton symmetry algebra.

Higher order singletons, partially massless fields and their boundary values in the ambient approach