Generalized AdS/CFT dualities and unitary realizations of space-time symmetries of M-theory

I review the AdS/CFT (anti-de Sitter/conformal field theory) dualities with in the framework of the general theory of unitary lowest-weight (ULWR) (pos itive-energy) representations of non-compact spacetime groups and supergrou ps. The ULWRs have the remarkable property that they can be constructed by tensoring some fundamental ULWRs (singletons or doubletons). The conformall y invariant theory in d dimensions to which M/superstring theory over AdS(( d+1)) x S-P is dual to is a singleton or doubleton field theory. One can wo rk either in a manifestly unitary compact 'particle' basis (Wigner picture) or manifestly covariant non-compact 'coherent state' basis (Dirac picture) of the ULWRs of conformal (super)groups. These coherent states are labelle d by spacetime coordinates and correspond to covariant fields with definite conformal dimensions. On the other hand, the supercoherent states of the U LWRs of superconformal algebras correspond to superfields. These results ex tend to higher-dimensional generalized spacetimes (superspaces) defined by Jordan (super)algebras and Jordan (super)triple systems. In particular, the y extend to the ULWRs of the M-theory symmetry superalgebra OSp(1/32, R).