Singletons, doubletons and M-theory

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) × Sp(2, ℝ) of OSp(16/2, ℝ) corresponds to the AdS extension of the Poincaré 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 AdS2. 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 11d and type IIB supergravity theories compactified over various spheres in terms of singleton or doubleton supermultiplets of corresponding AdS supergroups.