Conformal Higher Spin Symmetries of 4d Massless Supermultiplets and $osp(L,2M)$ Invariant Equations in Generalized (Super)Space

TL;DR

The paper develops an unfolded, covariant description of free 4d massless supermultiplets with conformal higher spin symmetry, realized on Fock-modules dual to unitary doubletons of $su(2,2)$ and extended to $osp(L,2M)$-invariant generalized spaces. A Bogolyubov-type duality links nonunitary field-theory modules to unitary singleton representations, providing a unitarity-consistent quantization route for the $sp(2M)$-covariant dynamics and clarifying the spectrum across all spins. The framework yields explicit global higher spin transformations, worldline interpretations, and a proposed chain of AdS/CFT dualities across generalized symplectic spaces, suggesting a form of space-time dimension democracy. These results position $hu(m,n|8)$-type algebras and their self-conjugated reductions as the natural conformal higher spin symmetries for 4d massless multiplets and open avenues toward nonlinear higher spin dynamics and holography in generalized space-times.

Abstract

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