10 - The geometry of D-branes

Summary

As we have seen, branes of various sorts are solutions of string theory which are localised to some extent, and have well-defined mass and charge per unit volume. Since these masses and charges are measured at infinity, meaning that the branes are sources of fields from the massless sector, we might expect that they must be actually be solutions of the low energy equations of motion: the gravity sector and other fields such as the various antisymmetric tensor fields, and possibly the dilaton. These field configurations can be thought of as representing interesting backgrounds in which the string can propagate. It has become increasingly important in many recent research areas to consider the details of such solutions, and we shall begin exploring this highly developed technology in the present chapter.

A look at black holes in four dimensions

Before we launch into a description of the solutions associated to branes, it is a good idea to start with something more familiar in order to gain some intuition about how the solutions work. We will start in four dimensions with a familiar system: Einstein's gravity coupled to Maxwell's electromagnetism. The more advanced reader may wish to skip directly to section 10.2 if the following is too elementary, but beware, since we shall be uncovering and emphasising probably less familiar features in order to prepare for analogous properties of branes in higher dimensions.