Quantum field theory has traditionally concerned the quantisation of point particles and so far this book has largely been about the classical, and then quantum, behaviour of strings. In this chapter we will consider objects that sweep out, as they move through space-time, spatial volumes of dimension greater than 1. We refer to such an object as being a p-brane if its world volume contains time and p spatial coordinates. A 0-brane is just a particle and a 1-brane is a string. In fact, p-branes for p ≥ 2 occur in string theory as solitons in the corresponding low energy effective actions of string theories as well as 0-branes and 1-branes. Indeed, we found in section 13.8 that the IIA and IIB supergravities, which are the unique low energy effective actions for the IIA and IIB superstring theories, each have a whole family of p-brane solutions. Being solitons, p-branes are non-perturbative objects as seen from the perspective of the low energy effective actions, and, except for the fundamental strings, are non-perturbative from the viewpoint of string perturbation theory.

In this chapter, we will study p-branes as objects in their own right and, using supersymmetry, we will find what possible superbranes can exist and give their dynamics. We will see later in this book that p-branes are related by duality symmetries to the perturbative strings that we studied earlier. As such, string duality symmetries imply that string theory should be extended to a theory that includes branes on an equal footing with strings.