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Foreword Preface Notation 10 Type I and type II superstrings 10.1 The superconformal algebra 10.2 Ramond and Neveu-Schwarz sectors 10.3 Vertex operators and bosonization 10.4 The superconformal ghosts 10.5 Physical states 10.6 Superstring theories in ten dimensions 10.7 Modular invariance 10.8 Divergences of type I theory Exercises 11 The heterotic string 11.1 World-sheet supersymmetries 11.2 The SO(32) and E8 x E8 heterotic strings 11.3 Other ten-dimensional heterotic strings 11.4 A little Lie algebra 11.5 Current algebras 11.6 The bosonic construction and toroidal compactification Exercises 12 Superstring interactions 12.1 Low energy supergravity 12.2 Anomalies 12.3 Superspace and superfields 12.4 Tree-level amplitudes 12.5 General amplitudes 12.6 One-loop amplitudes Exercises 13 D-branes 13.1 T-duality of type II strings 13.2 T-duality of type I strings 13.3 The D-brane charge and action 13.4 D-brane interactions: statics 13.5 D-brane interactions: dynamics 13.6 D-brane interactions: bound states Exercises 14 Strings at strong coupling 14.1 Type IIB string and SL(2,Z) duality 14.2 U-duality 14.3 SO(32) type I-heterotic duality 14.4 Type IIA string and M-theory 14.5 The E8 x Es heterotic string 14.6 What is string theory? 14.7 Is M for matrix? 14.8 Black hole quantum mechanics Exercises 15 Advanced CFT 15.1 Representations of the Virasoro algebra 15.2 The conformal bootstrap 15.3 Minimal models 15.4 Current algebras 15.5 Coset models 15.6 Representations of the N=1 superconformal algebra 15.7 Rational CFT 15.8 Renormalization group flows 15.9 Statistical mechanics Exercises 16 Orbifolds 16.1 Orbifolds of the heterotic string 16.2 Spacetime supersymmetry 16.3 Examples 16.4 Low energy field theory Exercises 17 Calabi-Yau compaetification 17.1 Conditions for N=1 supersymmetry 17.2 Calabi-Yau manifolds 17.3 Massless spectrum 17.4 Low energy field theory 17.5 Higher corrections 17.6 Generalizations 18 Physics in four dimensions 18.1 Continuous and discrete symmetries 18.2 Gauge symmetries 18.3 Mass scales 18.4 More on unification 18.5 Conditions for spacetime supersymmetry 18.6 Low energy actions 18.7 Supersymmetry breaking in perturbation theory 18.8 Supersymmetry beyond perturbation theory Exercises 19 Advanced topics 19.1 The N=2 superconformal algebra 19.2 Type II strings on Calabi-Yau manifolds 19.3 Heterotic string theories with (2,2) SCFT 19.4 N=2 minimal models 19.5 Gepner models 19.6 Mirror symmetry and applications 19.7 The conifold 19.8 String theories on K3 19.9 String duality below ten dimensions 19.10 Conclusion Exercises Appendix B: Spinors and SUSY in various dimensions B.1 Spinors in various dimensions B.2 Introduction to supersymmetry: d=4 B.3 Supersymmetry in d -- 2 B.4 Differential forms and generalized gauge fields B.5 Thirty-two supersymmetries B.6 Sixteen supersymmetries B.7 Eight supersymmetries Exercises References Glossary Index