A stable supermembrane vacuum with a discrete spectrum

We examine the massless spectrum of the supermembrane in the background of four-dimensional anti-de Sitter space times a compact internal space, by considering quantisation about a collapsed membrane configuration. We also observe that the vacuum is stable and that the spectrum of massive states is necessarily discrete. In this respect, the supermembrane favours anti-de Sitter over Minkowski space, where the spectrum seems likely to be continuous. (author). 19 refs