Abstract :
The supermembrane theory on R10 × S1 is investigated for membranes that wrap once around the compact dimension. The Hamiltonian can be organized as describing Ns interacting strings, the exact supermembrane corresponding to Ns → ∞. The zero-mode part of Ns − 1 strings turns out to be precisely the modes which are responsible for instabilities. For sufficiently large compactification radius R0, 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 g2 → ∞, where g2 ≡ 4π2T3R03 and T3 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.
