## Séminaire de Physique Théorique

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

Maxim Grigoriev (Moscou)

Thursday 06 June 2013 14:00 - Tours - Salle 1180 (Bât E2)

**Résumé :**

Using ambient space we develop a fully gauge and $\mathfrak{o}(d,2)$ 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) Fradkin--Tseytlin 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 of odd depths described by the Vasiliev equations based on the higher-order singleton symmetry algebra.

**Liens :**