Supermembrane dynamics from multiple interacting strings

Abstract

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 $g^2\equiv 4π^2 T_3 R_0^3$ 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.