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

We study the unitary supermultiplets of the N = 4 d = 7 anti-de Sitter (AdS(7)) superalgebra OSp(8*/4), with the even subalgebra SO(6, 2) x USp(4), which is the symmetry superalgebra of M-theory on AdS(7) x S-4. We give a complete classification of the positive energy doubleton and massless supermultiplets of OSp(8*/4). The ultra-shea doubleton supermultiplets do not have the Poincare 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 Poincare mass operator m(2) = PmuPmu 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) x 2> (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*14) can be given a dynamical realization in terms of chiral super-twister fields. (C) 2000 Elsevier Science B.V. All rights reserved.