Gravity and Strings

14
String theory
In this chapter we start the study of the extended objects that appear in the non-perturbative
spectrum of string theory, the subject of the third part of this book. In this part we will make
use of all the techniques we have developed in the first and second parts, whose main goal
wastoserve as a preparation for the third.
In a certain sense, this third part also presents the synthesis and (it is hoped) culmination
of the ideas presented in the previous two in the framework of string theory: on the
one hand, string theory includes a presumably consistent theory of quantum gravity that
contains the gravitons described at lowest order by the Fierz–Pauli theory we studied in
Chapter 3 [833, 834]. There are two main differences from the non-renormalizable theory
of GR: the presence of a dimensionless coupling constant different from the Planck length
and the presence of terms of higher order in derivatives. Furthermore, consistent string
theories have spacetime supersymmetry and, therefore, supergravity, which we studied in
Chapters 5 and 13. On the other hand, string theory incorporates naturally extra dimensions
that have to be compactified. Thus, the ideas of Kaluza and Klein studied in Chapter 11 are
also integrated into the picture.
Finally, the Schwarzschild, Reissner–Nordström, pp-wave, etc. solutions studied in other
chapters are also solutions of string theory and it is natural to try to use them to solve the
puzzles that arise when one tries to do quantum mechanics in those backgrounds: the information
and entropy problems. If string theory is really a good theory of quantum gravity,
then it should help us to solve them and we will see to what extent it succeeds in the last
chapter (Chapter 20) of this part.
The attempts to solve these long-standing problems have been made possible by recent
developments in string theory (essentially dualities and D-branes) and also by a change of
perspective that we could call the “spacetime approach,” which is based on the effectivefield
theories, when further advance with the “worldsheet approach” was becoming increasingly
difficult and slow. Of course, the two approaches are complementary and there has
been a considerable amount of feedback between them. In fact, some of the most interesting
things that we have learned in this period are the relations between the two of them. The
logic of these relations is represented schematically in Figure 14.1 and it is worth pausing
for a moment to describe it in detail.
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