Compactifications of the eleven-dimensional supermembrane

We construct new vacua for the eleven-dimensional supermembrane in which spacetime is the product of four-dimensional anti-de Sitter space and a compact seven-dimensional Einstein space, and the membrane is a sphere of non-zero radius in the anti-de Sitter space. In one class of solution the radius is a specific multiple of the anti-de Sitter scale parameter while in a second class the radius is arbitrary. Remarkably, only two of the Freund-Rubin compactifications admit vacua of the latter class: the round seven-sphere with N=8 supersymmetry and the N(0,1) space with N=3 supersymmetry. (author). 27 refs