Supersymmetric extended objects

Typescript (photocopy).Some recent advances in supermembrane theory are reported in detail, mainly concerning the heterotic fivebrane, string/fivebrane duality, the new Type II supermembranes and associated topics. In analogy with the Dirac magnetic monopole, the elementary string is found as the electric-like singular solution to the field-theory limit of the heterotic string but as the magnetic-like singular solution to the field-theory limit of the heterotic fivebrane, and vice versa for the elementary fivebrane. Moreover, in analogy with the 't Hooft-Polyakov monopole, not only does the heterotic string admit the heterotic fivebrane as a soliton but the heterotic fivebrane admits as a soliton a heterotic string. Furthermore, since the heterotic fivebrane has been shown to be an exact solution of the heterotic string, its existence has been confirmed as an inevitable consequence of string theory. All this gives strong support that there may be a duality between the heterotic string and the heterotic fivebrane in the sense that both of them describe the same physics. It is also shown that string/fivebrane duality implies that the quantum effect of the string corresponds to the classical behavior of the fivebrane and vice versa. In addition, the new Type II supermembranes are found to exist, and the singular nature of the recently discovered solutions with curvature singularities at the origin is classified