ABSTRACT
The theory of p-branes, i.e. of p-dimensional extended objects, has attracted a lot of attention over the last few years. (The reader is referred to the review articles [411–413]). Such theories provide a natural generalization of the physics of string theories (p = 1). Among p-brane theories the supermembrane (p = 2) in eleven dimensions [414] has attracted the most interest since, like the super-string in ten dimensions, it is potentially consistent at the quantum level. There are a finite number of values of p and D for which it is classically possible to construct a space-time supersymmetric action which generalizes the Green-Schwarz superstring action to describe a D-dimensional extended object moving in a p-dimensional space-time [415, 458]. However, for values other than (p = 1, D = 10) and (p = 2, D = 11) such theories have incurable quantum anomalies [416–418].
