Aspects of Born-Infeld Theory and String/M-Theory

M/String Theory is the currently most popular approach to a unified quantum theory of gravity and the other interactions. We still lack a complete formulation of the theory, but there is a general consensus that whatever finally emerges it will involve in some way or to some degree of approximation, p− branes, i.e. p+1-dimensional Lorentzian submanifolds Σ of a Lorentzian spacetime manifold M . In M-theory one supposes that M is eleven dimensional. In string theory it is usually taken to be ten dimensional. Branes may crudely be sub-divided into two types Heavy and Light. In the former case one is usually thinking of many coincident branes whose gravitational field and hence the ambient spacetime metric is non-trivial. Semi-classically these may be studied using supergravity techniques. The other extreme is to study a single isolated brane moving in flat Minkowski spacetime as a solution of the Dirac-Born-Infeld equations of motion. This will be the approach taken in these lectures. It is well suited to newcomers to the subject because, as I will try to show, considerable insights into string theory can be gained by asking some of the simplest physical questions. There is little need for the full heavy technical machinery of supergravity or superstring theories. Thus the material is well suited for presentation at a School. I have deliberately tried to keep things simple. This runs the risk that experts may feel that I have not done full justice to the subject or indeed their contributions to it. If so, I apologize but I repeat my aim was to provide the beginner with a rapid survey of the subject. I will mainly assume that the brane is flat. It