How Unstable Are Fundamental Quantum Supermembranes?

Abstract

String duality requires the presence of solitonic $p$-branes. By contrast, the existence of fundamental supermembranes is problematic, since they are probably unstable. In this paper, we re-examine the quantum stability of fundamental supermembranes in 11 dimensions. Previously, supermembranes were shown to be unstable by approximating them with SU(n) super Yang-Mills fields as $n \rightarrow \infty$. We show that this instability persists even if we quantize the continuum theory from the very beginning. Second, we speculate how a theory of decaying membranes may still be physically relevant. We present some heuristic arguments showing that light membranes may be too short-lived to be detected, while very massive membranes, with longer lifetimes, may have only very weak coupling to the particles we see in nature. Either way, decaying membranes would not be detectable in the lab. (This article is to be published in Frontiers in Quantum Field Theory (World Scientific) dedicated to Keiji Kikkawa's 60th birthday.)