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

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 AdS d+1 /CF T d → AdS d /CF T d−1 →. .. dualities in the higher spin gauge theories is proposed.