Free fermionic higher spin fields in AdS(5)

TL;DR

This work formulates free, gauge-invariant actions for massless fermionic higher-spin fields in AdS$_5$ using the isomorphism $o(4,2)\simeq su(2,2)$ and an $su(2,2)$ multispinor description. By introducing oscillators and a compensator, the author constructs linearized higher-spin curvatures and an action principle that yields correct equations of motion upon extra-field decoupling, with the physical spectrum corresponding to a single spin $s+\tfrac{3}{2}$ field and DOF $N^s=2(s+2)$. The formalism unifies bosonic and fermionic higher-spin descriptions in AdS$_5$, setting the stage for supersymmetric extensions and interactions. The results provide a concrete, gauge-invariant framework for analyzing 5d higher-spin gauge theories at the free level and offer a path toward interacting, supersymmetric models.

Abstract

Totally symmetric massless fermionic fields of arbitrary spins in AdS(5) are described as su(2,2) multispinors. The approach is based on the well-known isomorfism o(4,2)=su(2,2). Explicitly gauge invariant higher spin free actions are constructed and free field equations are analyzed.