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-b ranes in the large n limit of Matrix theory. The Sp(2, R) factor in th e even subgroup SO(16) x Sp(2, R) of OSp(16/2, R) corresponds to the A dS extension of the Poincare symmetry of the longitudinal directions. The infinite number of D0-branes with ever increasing and quantized va lues of longitudinal momenta are identified with the Fourier modes of the singleton supermultiplets of OSp(16/2, R), which consist of 128 bo sons and 128 fermions. The large n limit of N = 16 U(n) Yang-Mills qua ntum mechanics which describes Matrix theory is a conformally invarian t 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-K lein supergravity theories in relation to the recent conjecture of Mal dacena relating the dynamics of n Dp-branes to certain AdS supergravit y theories. We point out the remarkable parallel between the conjectur e of Maldacena and the construction of the spectra of 11d and type IIB supergravity theories compactified over various spheres in terms of s ingleton or doubleton supermultiplets of corresponding AdS supergroups . (C) 1998 Elsevier Science B.V.