Conformal higher spin symmetries of 4-d massless supermultiplets and osp(L,2M) 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

{\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.

11.30.Ly
04.65.+e
11.25.Hf
field theory: conformal
massless
dimension: 4
multiplet
supersymmetry
spin: high
gauge field theory: Yang-Mills

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Figures(0)

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