When I first decided to write a book on string theory, more than ten years ago, my memories of my student years were much more vivid than they are today. Still, I remember that one of the greatest pleasures was finding a text that made a difficult subject accessible, and I hoped to provide the same for string theory.
Thus, my first purpose was to give a coherent introduction to string theory, based on the Polyakov path integral and conformal field theory.A second purpose was to show how some of the simplest four- dimensional string theories connect with previous ideas for unifying the Standard Model, and to collect general results on the physics of four- dimensional string theories as derived from world-sheet and spacetime symmetries.
Foreword
Preface
Notation
1 A first look at strings
1.1 Why strings?
1.2 Action principles
1.3 The open string spectrum
1.4 Closed and unoriented strings
Exercises
2 Conformal field theory
2.1 Massless scalars in two dimensions
2.2 The operator product expansion
2.3 Ward identities and Noether's theorem
2.4 Conformal invariance
2.5 Free CFTs
2.6 The Virasoro algebra
2.7 Mode expansions
2.8 Vertex operators
2.9 More on states and operators
Exercises
3 The Polyakov path integral
3.1 Sums over world-sheets
3.2 The Polyakov path integral
3.3 Gauge fixing
3.4 The Weyl anomaly
3.5 Scattering amplitudes
3.6 Vertex operators
3.7 Strings in curved spacetime
Exercises
4 The string spectrum
4.1 Old covariant quantization
4.2 BRST quantization
4.3 BRST quantization of the string
4.4 The no-ghost theorem
Exercises
5 The string S-matrix
5.1 The circle and the toms
5.2 Moduli and Riemann surfaces
5.3 The measure for moduli
5.4 More about the measure
Exercises
6 Tree-level amplitudes
6.1 Riemann surfaces
6.2 Scalar expectation values
6.3 The bc CFT
6.4 The Veneziano amplitude
6.5 Chan-Paton factors and gauge interactions
6.6 Closed string tree amplitudes
6.7 General results
Exercises
7 One-loop amplitudes
7.1 Riemann surfaces
7.2 CFT on the toms
7.3 The toms amplitude
7.4 Open and unoriented one-loop graphs
Exercises
8 Toroidal eompaetifieation and T-duality
8.1 Toroidal compactification in field theory
8.2 Toroidal compactification in CFT
8.3 Closed strings and T-duality
8.4 Compactification of several dimensions
8.5 Orbifolds
8.6 Open strings
8.7 D-branes
8.8 T-duality of unoriented theories
Exercises
9 Higher order amplitudes
9.1 General tree-level amplitudes
9.2 Higher genus Riemann surfaces
9.3 Sewing and cutting world-sheets
9.4 Sewing and cutting CFTs
9.5 General amplitudes
9.6 String field theory
9.7 Large order behavior
9.8 High energy and high temperature
9.9 Low dimensions and noncritical strings
Exercises
Appendix A: A short course on path integrals
A.1 Bosonic fields
A.2 Fermionic fields
Exercises
References
Glossary
Index
