Realization of the conformal higher spin symmetry on the 4d massless field
supermultiplets is given. The self-conjugated supermultiplets, including the
linearized 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(2N,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
AdSd+1/CFTd→AdSd/CFTd−1→... dualities in the higher spin
gauge theories is proposed.Comment: Latex, 63 pages; no figures.V2 Typos corrected, References updated.
V3.Typos correced, references and an explanation on the relationship with
previous work in section 4 are added. The version to appear in Phys.Rev.