Generalized Ads/cft Dualities and Space-time Symmetries of M/superstring Theory

I review the relationship between AdS/CFT ( anti-de Sitter / conformal field theory) dualities and the general theory of unitary lowest weight (ULWR) (positive energy) representations of non-compact space-time groups and supergroups. The ULWR’s have the remarkable property that they can be constructed by tensoring some fundamental ULWR’s ( singletons or doubletons). Furthermore, one can go from the manifestly unitary compact basis of the ULWR’s of the conformal group ( Wigner picture) to the manifestly covariant coherent state basis ( Dirac picture) labelled by the space-time coordinates. Hence every irreducible ULWR corresponds to a covariant field with a definite conformal dimension. These results extend to higher dimensional generalized spacetimes ( superspaces) defined by Jordan (super) algebras and Jordan (super) triple systems. In particular, they extend to the ULWR’s of the M-theory symmetry superalgebra OSp(1/32,R). Invited talk given at the IXth Marcel Grossmann Meeting in Rome, July,