The Osp(8|4) singleton action from the supermembrane

Abstract

Our goal is to study the supermembrane on an $Ad{S}_4\times {\mathcal{M}}_7$ background, where ${\mathcal{M}}_7$ is a 7--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 ${\mathcal{M}}_7={\mathcal{S}}^7$. We find the explicit form of the action of the membrane coupled to this background geometry and show its invariance under non--linearly realised superconformal transformations. To do this we introduce a supergroup generalisation of the solvable Lie algebra parametrisation 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 realised as a free field theory living on flat Minkowski space.

36 pages, 2 figures, LaTex, uses package latexsym. Improved the text with some clarifications, references and equations added

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• M 5-brane and superconformal (0,2) tensor multiplet in 6 dimensions
• Special Conformal Symmetry of Worldvolume Actions
• Conformal Symmetry on World Volumes of Branes

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