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Preface Acknowledgments ¢ñ First Quantization and Path Integrals 1 Path Integrals and Point Particles 1.1 Why Strings? 1.2 Historical Review of Gauge Theory 1.3 Path Integrals and Point Particles 1.4 Relativistic Point Particles 1.5 First and Second Quantization 1.6 Faddeev-Popov Quantization 1.7 Second Quantization 1.8 Harmonic Oscillators 1.9 Currents and Second Quantization 1.10 Summary References 2 Nambu-Goto Strings 2.1 Bosonic Strings 2.2 Gupta-Bleuler Quantization 2.3 Light Cone Quantization 2.4 BRST Quantization 2.5 Trees 2.6 From Path Integrals to Operators 2.7 Projective Invariance and Twists 2.8 Closed Strings 2.9 Ghost Elimination 2.100 Summary References 3 Superstrings 3.1 Supersymmetric Point Particles 3.2 Two-Dimensional Supersymmetry 3.3 Trees 3.4 Local Two-Dimensional Supersymmetry 3.5 Quantization 3.6 GSO Projection 3.7 Superstrings 3.8 Light Cone Quantization of the GS Action 3.9 Vertices and Trees 3.10 Summary References 4 Conformal Field Theory and Kac¡ª¡ªMoody Algebras 4.1 Conformal Field Theory 4.2 Superconformal Field Theory 4.3 Spin Fields 4.4 Superconformal Ghosts 4.5 Fermion Vertex 4.6 Spinors and Trees 4.7 Kac-Moody Algebras 4.8 Supersymmetry 4.9 Summary References 5 Mulfiloops and Teichmuller Spaces 5.1 Unitarity 5.2 Single-Loop Amplitude 5.3 Harmonic Oscillators 5.4 Single-Loop Superstring Amplitudes 5.5 Closed Loops 5.6 Multiloop Amplitudes 5.7 Riemann Surfaces and Teichmiiller Spaces 5.8 Conformal Anomaly 5.9 Superstrings 5.10 Determinants and Singularities 5.11 Moduli Space and Grassmannians 5.12 Summary References ¢ò Second Quantization and the Search for Geometry 6 Light Cone Field Theory 6.1 Why String Field Theory? 6.2 Deriving Point Particle Field Theory 6.3 Light Cone Field Theory 6.4 Interactions 6.5 Neumann Function Method 6.6 Equivalence of the Scattering Amplitudes 6.7 Four-String Interaction 6.8 Superstring Field Theory 6.9 Summary References 7 BRST Field Theory 7.1 Covariant String Field Theory 7.2 BRST Field Theory 7.3 Gauge Fixing 7.4 Interactions 7.5 Witten's String Field Theory 7.6 Proof of Equivalence 7.7 Closed Strings and Superstrings 7.8 Summary References ¢ó Phenomenology and Model Building 8 Anomalies and the Atiyah-Singer Theorem 8.1 Beyond GUT Phenomenology 8.2 Anomalies and Feynman Diagrams 8.3 Anomalies in the Functional Formalism 8.4 Anomalies and Characteristic Classes 8.5 Dirac Index 8.6 Gravitational and Gauge Anomalies 8.7 Anomaly Cancellation in Strings 8.8 Summary References 9 Heterotic Strings and Compactification 9.1 Compactification 9.2 The Heterotic String 9.3 Spectrum 9.4 Covariant and Fermionic Formulations 9.5 Trees 9.6 Single-Loop Amplitude 9.7 Es and Kac¡ª¡ªMoody Algebras 9.8 Lorentzian Lattices 9.9 Summary References 10 Calabi¡ª¡ªYau Spaces and Orbifolds 10.1 Calabi-Yau Spaces 10.2 Review of de Rahm Cohomology 10.3 Cohomology and Homology 10.4 K/ihler Manifolds 10.5 Embedding the Spin Connection 10.6 Fermion Generations 10.7 Wilson Lines 10.8 Orbifoids 10.9 Four-Dimensional Superstrings 10.10 Summary References ¢ô M-Theory 11 M-Theory and Duality 11.1 Introduction 11.2 Duality in Physics 11.3 Why Five String Theories? 11.4 T-Duality 11.5 S-Duality 11.5.1 Type IIA Theory 11.5.2 Type IIB Theory 11.5.3 M-Theory and Type IIB Theory 11.5.4 E8 E8 Heterotic String 11.5.5 Type I Strings 11.6 Summary References 12 Compactifications and BPS States 12.1 BPS States 12.2 Supersymmetry and P-Branes 12.3 Compactification 12.4 Example: D = 6 12.4.1 D = 6, N = (2, 2) Theory 12.4.2 D = 6, N = (1, 1) Theories 12.4.3 M-Theory in D = 7 12.5 Example:D=4, N=2 and D=6, N=1 12.6 Symmetry Enhancement and Tensionless Strings 12.7 F-Theory 12.8 Example: D = 4 12.9 Summary References 13 Solitons, D-Branes, and Black Holes 13.1 Solitons 13.2 Supermembrane Actions 13.3 Five-Brahe Action 13.4 D-Branes 13.5 D-Brane Actions 13.6 M(atrix) Models and Membranes 13.7 Black Holes 13.8 Summary 13.9 Conclusion References Appendix A.1 A Brief Introduction to Group Theory A.2 A Brief Introduction to General Relativity A.3 A Brief Introduction to the Theory of Forms A.4 A Brief Introduction to Supersymmetry A.5 A Brief Introduction to Supergravity A.6 Notation References Index