Flato-Fronsdal theorem for higher-order singletons

Understand

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.