The Osp(8 vertical bar 4) singleton action from the supermembrane

Our goal is to study the supermembrane on an AdS(4) x M-7 background, where M-7 is a seven-dimensional Einstein manifold with N Killing spinors, This is a direct way to derive the Osp(N\4) singleton field theory with all the additional properties inherited from the geometry of the internal manifold, As a first example we consider the maximally supersymmetric Osp(8\4) singl eton corresponding to the choice M-7 = S-7. We find the explicit form of th e action of the membrane coupled to this background geometry and show its i nvariance under non-linearly realized superconformal transformations, To do this we introduce the supergroup generalization of the solvable Lie algebr a parametrization of non-compact coset spaces. We also derive the action of quantum fluctuations around the classical configuration, showing that this is precisely the singleton action, We find that the singleton is simply re alized as a free field theory living on flat Minkowski space, (C) 1999 Else vier Science B.V.