Unitary Supermultiplets of OSp(1/32,R) and M-theory
Murat Gunaydin
TL;DR
The work develops an oscillator-based construction of unitary lowest-weight representations for the maximal AdS-like supergroup relevant to M-theory, OSp(1/32,R). It shows that parity-invariant left-right extensions contract to the 11D Poincaré superalgebra with central charges, with doubleton sectors generating the full massless AdS11 supermultiplets; the CPT self-conjugate doubleton is central to this structure. The author argues that a ten-dimensional CPT self-conjugate doubleton field theory serves as the holographic dual to an AdS phase of M-theory, analogously to N=4 SYM in d=4 being dual to IIB on AdS5×S5, thus extending holographic ideas to maximal spacetime dimensions. The paper thus links the representation theory of OSp(1/32,R) to the field content of 11D supergravity and proposes a ten-dimensional boundary theory as the holographic underpinning of M-theory in AdS-like backgrounds. Overall, it provides a rigorous framework for exploring AdS/CFT-type dualities in the maximal dimension block and for understanding how doubleton and singleton sectors encode the spectrum of M-theory excitations.
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.