Conformal higher spin symmetries of 4D massless supermultiplets andosp(L,2M)invariant equations in generalized (super)space

Abstract

Realization of the conformal higher spin symmetry on the 4D massless field supermultiplets is given. The self-conjugated supermultiplets, including the linearized $\mathcal{N}=4$ super Yang-Mills theory, are considered in some detail. Duality between nonunitary field-theoretical representations and the unitary doubleton-type representations of the 4D conformal algebra $\mathrm{su}(2,2)$ is formulated in terms of a Bogolyubov transform. The set of 4D massless fields of all spins is shown to form a representation of $\mathrm{sp}(8).$ The results obtained are extended to the generalized superspace invariant under $\mathrm{osp}(L,2M)$ supersymmetries. A world line particle interpretation of the free higher spin theories in the $osp(2\mathcal{N},2M)$ invariant (super)space is given. Compatible with unitarity, free equations of motion in the $\mathrm{osp}(L,2M)$ invariant (super)space are formulated. A conjecture about the chain of ${\mathrm{AdS}}_{d+1}/{\mathrm{CFT}}_{d}\ensuremath{\rightarrow}{\mathrm{AdS}}_{d}/{\mathrm{CFT}}_{d\ensuremath{-}1}\ensuremath{\rightarrow}\ensuremath{\cdot}\ensuremath{\cdot}\ensuremath{\cdot}$ (where CFT indicates conformal field theory) dualities in the higher spin gauge theories is proposed.