Supermembrane dynamics from multiple interacting strings

TL;DR

This paper explores supermembrane dynamics on a compact space, showing how it relates to multiple interacting strings and how the spectrum transitions from membrane to string behavior as the compactification radius varies.

Contribution

It provides a detailed analysis of supermembrane interactions and spectrum, connecting membrane theory to string theory in different limits and revealing the role of instabilities.

Findings

At large radius, interactions are negligible and spectrum is harmonic oscillator-like.

In the zero-radius limit, the spectrum matches type IIA superstring spectrum with additional states.

The spectrum transitions from membrane to string behavior as the compactification radius decreases.

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 $g^2\equiv 4\pi^2 T_3 R_0^3$ 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.