The goal of these two volumes is to provide a complete introduction to string theory, starting at the beginning and proceeding through the compactification to four dimensions and to the latest developments in strongly coupled strings.
Volume one is an introduction to bosonic string theory. This is not a realistic theory --- it does not have fermions, and as far as is known has no stable ground state. The philosophy here is the same as in starting a course on quantum field theory with a thorough study of scalar field theory. That is also not the theory one is ultimately interested in, but it provides a simple example for developing the unique dynamical and technical features of quantum field theory before introducing the complications of spin and gauge invariance. Similarly, a thorough study of bosonic string theory will give us a framework to which we can in short order add the additional complications of fermions and supersymmetry.
Chapter 1 is introductory. We present first the action principle for the dynamics of string. We then carry out a quick and heuristic quantization using light-cone gauge, to show the reader some of the important aspects of the string spectrum. Chapters 2--7 are the basic introduction to bosonic string theory. Chapter 2 introduces the needed technical tools in the world-sheet quantum field theory, such as conformal invariance, the operator product expansion, and vertex operators. Chapters 3 and 4 carry out the covariant quantization of the string, starting from the Polyakov path integral. Chapters 5--7 treat interactions, presenting the general formalism and applying it to tree-level and one-loop amplitudes. Chapter 8 treats the simplest compactification of string theory, making some of the dimensions periodic. In addition to the phenomena that arise in compactified field theory, such as Kaluza--Klein gauge symmetry, there is also a great deal of `stringy' physics, including enhanced gauge symmetries, $T$-duality, and D-branes. Chapter 9 treats higher order amplitudes. The first half outlines the argument that string theory in perturbation theory is finite and unitary as advertised; the second half presents brief treatments of a number of advanced topics, such as string field theory. Appendix A is an introduction to path integration, so that our use of quantum field theory is self-contained.
Volume two treats supersymmetric string theories, focusing first on ten-dimensional and other highly symmetric vacua, and then on realistic four-dimensional vacua.
In chapters 10--12 we extend the earlier introduction to the supersymmetric string theories, developing the type I, II, and heterotic superstrings and their interactions. We then introduce the latest results in these subjects. Chapter 13 develops the properties and dynamics of D-branes, still using the tools of string perturbation theory as developed earlier in the book. Chapter 14 then uses arguments based on supersymmetry to understand strongly coupled strings. We find that the strongly coupled limit of any string theory is described by a dual weakly coupled string theory, or by a new eleven-dimensional theory known provisionally as M-theory. We discuss the status of the search for a complete formulation of string theory and present one promising idea, m(atrix) theory. We briefly discuss the quantum mechanics of black holes, carrying out the simplest entropy calculations. Chapter 15 collects a number of advanced applications of the various world-sheet symmetry algebras.
Chapters 16 and 17 present four-dimensional string theories based on orbifold and Calabi--Yau compactifications. The goal is not an exhaustive treatment but rather to make contact between the simplest examples and the unification of the Standard Model. Chapter 18 collects results that hold in wide classes of string theories, using general arguments based on world-sheet and spacetime gauge symmetries. Chapter 19 consists of advanced topics, including (2,2) world-sheet supersymmetry, mirror symmetry, the conifold transition, and the strong-coupling behavior of some compactified theories. Appendix B collects results on spinors and supersymmetry in various dimensions.
Annotated reference lists appear at the end of each volume. I have tried to assemble a selection of articles, particularly reviews, that may be useful to the student. A glossary also appears at the end of each volume.