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 was to serve 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 [1103, 1104]. 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 17. 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 15 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 Chapter 26.

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 effective field theories, when further advance with the “worldsheet approach” was becoming increasingly difficult and slow.