Supermembranes

TL;DR

This work surveys the theory of supermembranes and their extensions to p-branes, showing how supersymmetry, κ-symmetry, and dimensional reduction constrain allowed objects (brane scan) and connect 11D M-theory to 10D Type II strings. It develops both the classical worldvolume actions and the quantum aspects of membranes, highlighting area-preserving diffeomorphisms and the resulting matrix-model descriptions, as well as solitonic interpretations of branes as BPS states with dualities linking strings, membranes, and fivebranes. The text then elaborates on dualities: string/fivebrane duality in 10D, string/string duality in 6D, and the broader S- and T-duality framework, culminating in M-theory as the umbrella unifying picture that explains how membranes and fivebranes give rise to lower-dimensional strings under various compactifications. These dualities illuminate nonperturbative phenomena, black-brane physics, and potential routes to connecting different string theories into a single underlying structure with profound implications for quantum gravity and unification.

Abstract

We give an elementary introduction to the theory of supermembranes.