The Osp(8∥4) singleton action from the supermembrane Original Research Article

Our goal is to study the supermembrane on an AdS4 × M7 background, where M7 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) singleton corresponding to the choice M7 = S7. We find the explicit form of the action of the membrane coupled to this background geometry and show its invariance under non-linearly realized superconformal transformations. To do this we introduce the supergroup generalization of the solvable Lie algebra 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 realized as a free field theory living on flat Minkowski space.