Singletons, Doubletons and M-theory

TL;DR

The paper develops a framework in which singleton and doubleton representations of AdS supergroups organize the spectrum of M-theory and Matrix theory. It identifies the two-dimensional AdS subsupergroup $OSp(16/2,R)$ inside $OSp(1/32,R)$ and shows that its singleton content encodes the dynamics of $D0$-branes in the large-$n$ limit of Matrix theory, with the singleton quantum mechanics living on the boundary of $AdS_{2}$. Using the oscillator method, it demonstrates how tensor products of singleton/doubleton multiplets generate the infinite Kaluza–Klein towers and bulk massless multiplets, connecting these boundary theories to bulk AdS supergravity spectra and Maldacena’s AdS/CFT paradigm. Across various AdS compactifications, the work highlights a parallel between the boundary singleton/doubleton theories and the bulk spectra of $11$-d and type $IIB$ supergravity, suggesting a unified boundary-based description of M-theory dynamics in the large-$n$ limit of Matrix theory.

Abstract

We identify the two dimensional AdS subsupergroup $OSp(16/2,R)$ of the M-theory supergroup $OSp(1/32,R)$ which captures the dynamics of $n$ $D0$-branes in the large $n$ limit of Matrix theory. The $Sp(2,R)$ factor in the even subgroup $SO(16) \times Sp(2,R)$ of $OSp(16/2,R)$ corresponds to the AdS extension of the Poincare symmetry of the longitudinal directions. The infinite number of $D0$-branes with ever increasing and quantized values of longitudinal momenta are identified with the Fourier modes of the singleton supermultiplets of $OSp(16/2,R)$,which consist of 128 bosons and 128 fermions. The large $n$ limit of N=16 U(n) Yang-Mills quantum mechanics which describes Matrix theory is a conformally invariant N=16 singleton quantum mechanics living on the boundary of $AdS_{2}$. We also review some of the earlier results on the spectra of Kaluza-Klein supergravity theories in relation to the recent conjecture of Maldacena relating the dynamics of $n$ $Dp$-branes to certain AdS supergravity theories. We point out the remarkable parallel between the conjecture of Maldacena and the construction of the spectra of $11-d$ and type $IIB$ supergravity theories compactified over various spheres in terms of singleton or doubleton supermultiplets of corresponding AdS supergroups.