Abstract :
We review the oscillator construction of the unitary representations of non-compact groups and supergroups and study the unitary supermultiplets of OSp(132, R) in relation to M-theory. OSp(132,R) has a singleton supermultiplet consisting of a scalar and a spinor field. Parity invariance leads us to consider OSp(132, R)L × OSp(132, R)R as the “minimal” generalized AdS supersymmetry algebra of M-theory corresponding to the embedding of two spinor representations of SO(10, 2) in the fundamental representation of Sp(32,R). The contraction to the Poincaré superalgebra with central charges proceeds via a diagonal subsupergroup OSp(132, R)L−R which contains the common subgroup SO(10, 1) of the two SO(10, 2) factors. The parity invariant singleton supermultiplet of OSp(132, R)L × OSp(132, R)R decomposes into an infinite set of “doubleton” supermultiplets of the diagonal OSp(132, R)L−R. There is a unique “CPT self-conjugate” doubleton supermultiplet whose tensor product with itself yields the “massless” generalized AdS11 supermultiplets. The massless graviton supermultiplet contains fields corresponding to those of eleven-dimensional supergravity plus additional ones. Assuming that an AdS phase of M-theory exists we argue that the doubleton field theory must be the holographic superconformal field theory in ten dimensions that is dual to M-theory in the same sense as the duality between the N = 4 super-Yang-Mills in d = 4 and the IIB superstring over AdS5 × S5.
