2 - The bosonic string

Summary

This chapter introduces the simplest string theory, called the bosonic string. Even though this theory is unrealistic and not suitable for phenomenology, it is the natural place to start. The reason is that the same structures and techniques, together with a number of additional ones, are required for the analysis of more realistic superstring theories. This chapter describes the free (noninteracting) theory both at the classical and quantum levels. The next chapter discusses various techniques for introducing and analyzing interactions.

A string can be regarded as a special case of a p-brane, a p-dimensional extended object moving through space-time. In this notation a point particle corresponds to the p = 0 case, in other words to a zero-brane. Strings (whether fundamental or solitonic) correspond to the p = 1 case, so that they can also be called one-branes. Two-dimensional extended objects or two-branes are often called membranes. In fact, the name p-brane was chosen to suggest a generalization of a membrane. Even though strings share some properties with higher-dimensional extended objects at the classical level, they are very special in the sense that their two-dimensional world-volume quantum theories are renormalizable, something that is not the case for branes of higher dimension. This is a crucial property that makes it possible to base quantum theories on them. In this chapter we describe the string as a special case of p-branes and describe the properties that hold only for the special case p = 1.