Unitary supermultiplets of OSp(8^*|4) and the AdS₇/CFT₆ duality

We study the unitary supermultiplets of the N=4d=7 anti-de Sitter ( AdS₇ ) superalgebra OSp(8^*|4) , with the even subalgebra SO(6,2)×USp(4) , which is the symmetry superalgebra of M-theory on AdS₇×S⁴ . We give a complete classification of the positive energy doubleton and massless supermultiplets of OSp(8^*|4) . The ultra-short doubleton supermultiplets do not have the Poincaré limit in AdS₇ and correspond to superconformal field theories on the boundary of AdS₇ which can be identified with d=6 Minkowski space. We show that the six-dimensional Poincaré mass operator m²=P_μP^μ vanishes identically for the doubleton representations. By going from the compact U(4) basis of SO^*(8)=SO(6,2) to the noncompact basis SU^*(4)×D (d=6 Lorentz group times dilatations) one can associate the positive (conformal) energy representations of SO^*(8) with conformal fields transforming covariantly under the Lorentz group in d=6 . The oscillator method used for the construction of the unitary supermultiplets of OSp(8^*|4) can be given a dynamical realization in terms of chiral super-twistor fields.