Gravity and Strings

18
Extended objects
Introduction
In the previous chapters we have studied the upper-left- and upper-right-hand boxes of
Figure 14.1 that concern the standard perturbative formulation of string theory and the effective
actions of the ten-dimensional string theories (and M theory). We have also learned
a bit about the existence of some non-perturbative states in the string spectrum, in particular
D-branes and KK and winding modes in compactified theories (the lower-left-hand box
of Figure 14.1). We have studied in the three cases the existence of dualities that related
various theories and how these dualities are realized in the worldsheet action (when this is
possible, i.e. for T duality) and in the effective actions. We have also mentioned that S dualities
and T dualities imply the existence of new solitonic states in the string spectrum.
In this chapter and the next we are going to study systematically the lower-right-hand
and central boxes of Figure 14.1, that is, the solitonic solutions of the string effective-field
theories and their worldvolume actions. We will study the implications that the various dualities
have for them (which are evidently related to the effects of dualities on the effective
actions) and for the non-perturbative string spectrum. This chapter will be devoted to a general
introduction to extended objects and in the next chapter we will deal specifically with
those that occur in string/M theory.
These are subjects with many facets that are related in many ways to each other and to the
subjects of the previous chapters. Therefore, it is hopeless to try to give a complete, or even
half-complete, account of them in the space that we have at our disposal. Our aim will be to
cover the basic material and the essential results and solutions in a unified system of conventions
(like the rest of the book), giving pointers to the literature for further developments.
We start in Section 18.1 with a general introduction to the kinematics and dynamics of
generic extended objects in which we will discuss various forms of the actions for these
objects, their coupling to background fields (Section 18.1.1), and the generalization of the
Dirac quantization condition for extended objects (Section 18.1.2).
In Section 18.2 we treat the simplest generic black and extreme solutions of the “pbrane
a-model,” which is itself a generalization of the “a-model” studied in Section 12.1.
The string-theory solutions that we will study later are in general special cases of these
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