Unitary Supermultiplets of OSp(1/32,R) and M-theory

TL;DR

This paper explores the structure of unitary supermultiplets of the supergroup OSp(1/32,R) and their relation to M-theory, proposing a holographic duality with a superconformal field theory in ten dimensions.

Contribution

It introduces the oscillator construction of supermultiplets of OSp(1/32,R) and connects these to M-theory and AdS/CFT correspondence, highlighting the role of doubleton supermultiplets.

Findings

Singleton supermultiplet contains scalar and spinor fields.

Doubleton supermultiplets generate massless supermultiplets.

Proposes a holographic duality between doubleton field theory and M-theory.

Abstract

We review the oscillator construction of the unitary representations of noncompact groups and supergroups and study the unitary supermultiplets of OSp(1/32,R) in relation to M-theory. OSp(1/32,R) has a singleton supermultiplet consisting of a scalar and a spinor field. Parity invariance leads us to consider OSp(1/32,R)_L X OSp(1/32,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 Poincare superalgebra with central charges proceeds via a diagonal subsupergroup OSp(1/32,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(1/32,R)_L \times OSp(1/32,R)_R decomposes into an infinite set of "doubleton" supermultiplets of the diagonal OSp(1/32,R)_{L-R}. There is a unique "CPT self-conjugate" doubleton supermultiplet whose tensor product with itself yields the "massless" generalized AdS_{11} supermultiplets. The massless graviton supermultiplet contains fields corresponding to those of 11-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 AdS_5 X S^5.