Unitary supermultiplets of OSp(8∗|4) and the AdS7/CFT6 duality Original Research Article

We study the unitary supermultiplets of the N=4 d=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=PμPμ 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.