Singletons, Doubletons and M-theory

TL;DR

This paper explores the connection between M-theory, D0-branes, and AdS supergroups, identifying the singleton supermultiplets that describe the large N limit of Matrix theory and relating it to AdS/CFT correspondence.

Contribution

It identifies the AdS subsupergroup relevant to D0-branes in M-theory and relates singleton supermultiplets to the large N limit of Matrix theory, extending the understanding of AdS/CFT correspondence.

Findings

Identified the $OSp(16/2,R)$ supergroup as capturing D0-brane dynamics.

Connected singleton supermultiplets to the Fourier modes of D0-branes.

Reviewed spectra of supergravity theories in relation to AdS/CFT conjecture.

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.