Generalized AdS/CFT Dualities and Space-Time Symmetries of M/Superstring Theory

TL;DR

This paper explores the connection between AdS/CFT dualities and unitary representations of space-time groups, extending to higher dimensions and M-theory symmetries, revealing new insights into space-time and supersymmetry structures.

Contribution

It establishes a framework linking ULWRs of space-time groups to covariant fields, extending the theory to higher dimensions and M-theory superalgebras.

Findings

ULWRs can be constructed from fundamental ULWRs like singletons or doubletons.

Every ULWR corresponds to a covariant field with a specific conformal dimension.

Results extend to higher-dimensional superspaces and M-theory symmetry superalgebras.

Abstract

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).