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

TL;DR

This paper develops a covariant ambient space approach to analyze boundary values of AdS gauge fields, focusing on partially massless fields and higher-order conformal scalars, and proposes a generalized higher-spin holographic duality involving multicritical Lifshitz points.

Contribution

It introduces a gauge and covariant ambient space framework for boundary values of AdS fields, generalizes the Flato-Fronsdal theorem, and proposes a new higher-spin holographic duality involving higher-order singletons.

Findings

Identified Fradkin-Tseytlin equations as obstructions for boundary-to-bulk extension.

Related background fields for higher-order singletons to boundary values of partially massless fields.

Proposed a duality between the O(N) model at Lifshitz points and partially massless higher-spin theories.

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.