  The supermembrane theory on $R^{10}x S^1$ is investigated, for membranes that
wrap once around the compact dimension. The Hamiltonian can be organized as
describing $N_s$ interacting strings, the exact supermembrane corresponding to
$N_s\to \infty$. The zero-mode part of $N_s-1$ strings turn out to be precisely
the modes which are responsible of instabilities. For sufficiently large
compactification radius $R_0$, interactions are negligible and the
lowest-energy excitations are described by a set of harmonic oscillators. We
compute the physical spectrum to leading order, which becomes exact in the
limit $ g^2 \to \infty $, where $g^2\equiv 4\pi^2 T_3 R_0^3$ and $T_3$ is the
membrane tension. As the radius is decreased, more strings become strongly
interacting and their oscillation modes get frozen. In the zero-radius limit,
the spectrum is constituted of the type IIA superstring spectrum, plus an
infinite number of extra states associated with flat directions of the quartic
potential.

High Energy Physics - Theory