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

Abstract : Using ambient space we develop a fully gauge and o(d,2) covariant approach to boundary 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 the boundary. In particular, we identify the corresponding Fradkin-Tseytlin equations as obstructions to the extension of the off-shell boundary value to the bulk, generalizing the usual considerations for the holographic anomalies to the partially massless fields. We also relate the background fields for the higher-order singleton to the boundary values of partially massless fields and prove the appropriate generalization of the Flato-Fronsdal theorem, which is in agreement with the known structure of symmetries for the higher-order wave operator. All these facts support the following generalization of the higher-spin holographic duality: the O(N) model at a multicritical isotropic Lifshitz point should be dual to the theory of partially massless symmetric tensor fields described by the Vasiliev equations based on the higher-order singleton symmetry algebra.
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https://hal.archives-ouvertes.fr/hal-00878908
Contributor : Xavier Bekaert <>
Submitted on : Thursday, October 31, 2013 - 10:59:12 AM
Last modification on : Thursday, March 5, 2020 - 5:33:23 PM

### Citation

Xavier Bekaert, Maxim Grigoriev. Higher order singletons, partially massless fields and their boundary values in the ambient approach. Nuclear Physics B, Elsevier, 2013, 876, pp.667. ⟨10.1016/j.nuclphysb.2013.08.015⟩. ⟨hal-00878908⟩

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