Preface
Acknowledgments
Ⅰ 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——Moody 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
Ⅱ 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
Ⅲ 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——Moody Algebras
9.8 Lorentzian Lattices
9.9 Summary
References
10 Calabi——Yau Spaces and Orbifolds
10.1 Calabi-Yau Spaces
10.2 Review of de Rahm Cohomology
10.3 Cohomology and Homology
10.4 Kihler 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
Ⅳ 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 Matrix 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
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