Update on Supermembrane Theory

The D=11 maximally supersymmetric supermembrane is a theory ‘beyond’ string theory, and as such a candidate for non-perturbative unification (‘M theory’). In this talk I will review some of its basic features, such as its reformulation as a one-dimensional gauge theory of area preserving diffeomorhisms and the basic link to the SU(infty) matrix model of M theory. I will also review some more recent developments, in particular the question of how to set up a perturbative linearization suitable for a quantum mechanical path-integral treatment and the construction of ‘vertex operators’ for the massless states of the theory.