Flato-Fronsdal theorem for higher-order singletons

TL;DR

This paper extends the Flato-Fronsdal theorem to higher-order singletons, revealing a spectrum of partially-massless fields in higher-spin theories and proposing a new holographic duality with free higher-order scalar and spinor conformal field theories.

Contribution

It generalizes the Flato-Fronsdal theorem to higher-order singletons and suggests a novel holographic duality involving partially-massless fields and free conformal field theories.

Findings

Total Casimir energy vanishes at one loop.

Spectrum includes partially-massless fields of all depths.

Proposes a new holographic duality involving higher-order singletons.

Abstract

We prove a generalised Flato-Fronsdal theorem for higher-order, scalar and spinor, singletons. In the resulting infinite tower of bulk higher-spin fields, we point out the occurrence of partially-massless fields of all depths. This leads us to conjecture a holographic duality between a higher-spin gravity theory around $AdS_{d+1}$ with the aforementioned spectrum of fields, and a free $CFT_d$ of fundamental (higher-order) scalar and spinor singletons. As a first check of this conjecture, we find that the total Casimir energy vanishes at one loop.