Supermembrane dynamics from multiple interacting strings

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.Comment: Small corrections. 21 page

Stability of the quantum supermembrane in a manifold with boundary

We point out an effect which may stabilize a supersymmetric membrane moving on a manifold with boundary, and lead to a light-cone Hamiltonian with a discrete spectrum of eigenvalues. The analysis is carried out explicitly for a closed supermembrane in the regularized $SU(N)$ matrix model version.Comment: 10 pages, harvmac (references added, minor changes

T-duality in M-theory and supermembranes

The (q_1,q_2) SL(2,Z) string bound states of type IIB superstring theory admit two inequivalent (T-dual) representations in eleven dimensions in terms of a fundamental 2-brane. In both cases, the spectrum of membrane oscillations can be determined exactly in the limit $g^2\to \infty$, where $g^2$ is the type IIA string coupling. We find that the BPS mass formulas agree, and reproduce the BPS mass spectrum of the $(q_1,q_2)$ string bound state. In the non-BPS sector, the respective mass formulas apply in different corners of the moduli space. The axiomatic requirement of T-duality in M-theory permits to derive a discrete mass spectrum in a (thin torus) region where standard supermembrane theory undergoes instabilities.Comment: harvmac, 9 page