Abstract (Elsevier)
We give a rigorous proof that the quantum mechanical hamiltonians of a class of supersymmetric matrix models have a continuous spectrum starting at zero. We are thus led to conclude that supermembranes (which can be regarded as a limit of such models) have a continuous mass spectrum and, in particular, no mass gap. This result can be understood as a manifestation of the instability of the supermembrane against deformations into long stringlike configurations. We also comment upon possible implications of this result for supersymmetric Yang-Mills theories.