Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2001-01-22
Physics
High Energy Physics
High Energy Physics - Theory
Latex file, 11 pages; invited talk to appear in the Proceedings of the IXth Marcel Grossmann Meeting (Rome, July 2000)
Scientific paper
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).
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