Note: Cover -- Superstring TheoryVolume 1: Introduction 25th Anniversary Edition -- Dedication -- Title -- Copyright -- Contents -- Preface to the 25th Anniversary Edition -- 1. Introduction -- 1.1 The Early Days of Dual Models -- 1.1.1 The Veneziano amplitude and duality -- 1.1.2 High-energy behavior of the Veneziano model -- 1.1.3 Ramifications of the Veneziano model -- 1.2 Dual models of everything -- 1.2.1 Duality and the graviton -- 1.2.2 Unification in higher dimensions -- 1.2.3 Supersymmetry -- 1.3 String theory -- 1.3.1 The massless point particle -- 1.3.2 Generalization to strings -- 1.3.3 Constraint equations -- 1.4 String interactions -- 1.4.1 Splitting of strings -- 1.4.2 Vertex operators -- 1.4.3 Use of vertex operators -- 1.4.4 Evaluation of the scattering amplitude -- 1.4.5 The mass of the graviton -- 1.5 Other aspects of string theory -- 1.5.1 Gravitational Ward identities -- 1.5.2 Open strings -- 1.5.3 Internal symmetries of open strings -- 1.5.4 Recovery of the Veneziano amplitude -- 1.5.5 Comparison with QCD -- 1.5.6 Unitarity and gravity -- 1.6 Conclusion -- 2 Free bosonic strings -- 2.1 The classical bosonic string -- 2.1.1 String action and its symmetries -- 2.1.2 The free string in Minkowski space -- 2.1.3 Classical covariant gauge fixing and field equations -- 2.2 Quantization - old covariant approach -- 2.2.1 Commutation relations and mode expansions -- 2.2.2 Virasoro algebra and physical states -- 2.2.3 Vertex operators -- 2.3 Light-cone gauge quantization -- 2.3.1 Light-cone gauge and Lorentz algebra -- 2.3.2 Construction of transverse physical states -- 2.3.3 The no-ghost theorem andthe spectrum-generating algebra -- 2.3.4 Analysis of the spectrum -- 2.3.5 Asymptotic formulas for level densities -- 2.4 Summary -- 3 Modern covariant quantization -- 3.1 Covariant path-integral quantization -- 3.1.1 Faddeev-Popov ghosts. , 3.1.2 Complex world-sheet tensor calculus -- 3.1.3 Quantization of the ghosts -- 3.2 BRST quantization -- 3.2.1 Construction of BRST charge -- 3.2.2 Covariant calculation of the Virasoro anomaly -- 3.2.3 Virasoro, conformal and gravitational anomalies -- 3.2.4 Bosonization of ghost coordinates -- 3.3 Global aspects of the string world sheet -- 3.4 Strings in background fields -- 3.4.1 Introduction of a background space-time metric -- 3.4.2 Weyl invariance -- 3.4.3 Conformal invariance and the equations of motion -- 3.4.4 String-theoretic corrections to general relativity -- 3.4.5 Inclusion of other modes -- 3.4.6 The dilaton expectation value and the string coupling constant -- 3.5 Summary -- 4 World-sheet super symmetry in string theory -- 4.1 The classical theory -- 4.1.1 Global world-sheet supersymmetry -- 4.1.2 Superspace -- 4.1.3 Constraint equations -- 4.1.4 Boundary conditions and mode expansions -- 4.2 Quantization - the old covariant approach -- 4.2.1 Commutation relations and mode expansions -- 4.2.2 Super-Virasoro algebra and physical states -- 4.2.3 Boson-emission vertex operators -- 4.3 Light-cone gauge quantization -- 4.3.1 The light-cone gauge -- 4.3.2 No-ghost theorem and the spectrum-generating algebra -- 4.3.3 The GSO conditions -- 4.3.4 Locally supersymmetric form of the action -- 4.3.5 Superstring action and its symmetries -- 4.4 Modern covariant quantization -- 4.4.1 Faddeev-Popov ghosts -- 4.4.2 BRST symmetry -- 4.4.3 Covariant computation of the Virasoro anomaly -- 4.5 Extended world-sheet supersymmetry -- 4.5.1 The N = 2 theory -- 4.5.2 The N = 4 theory -- 4.6 Summary -- Appendix 4.A Super Yang-Mills Theories -- 5. Space-Time Supersymmetry in String Theory -- 5.1 The Classical Theory -- 5.1.1 The Superparticle -- 5.1.2 The Supersymmetric String Action -- 5.1.3 The Local Fermionic Symmetry. , 5.1.4 Type I and Type II Superstrings -- 5.2 Quantization -- 5.2.1 Light-Cone Gauge -- 5.2.2 Super-Poincare Algebra -- 5.3 Analysis of the Spectrum -- 5.3.1 Open Superstrings -- 5.3.2 Closed Superstrings -- 5.4 Remarks Concerning Covariant Quantization -- 5.5 Summary -- Appendix 5.A Properties of SO(2n) Groups -- Appendix 5.B The spin(8) Clifford Algebra -- 6. Nonabelian Gauge Symmetry -- 6.1 Open Strings -- 6.1.1 The Chan-Paton Method -- 6.2 Current Algebra on the String World Sheet -- 6.3 Heterotic Strings -- 6.3.1 The 50(32) Theory -- 6.3.2 The E8 x E8 Theory -- 6.4 Toroidal Compactification -- 6.4.1. Compactification on a Circle -- 6.4.2 Fermionization -- 6.4.3 Bosonized Description of the Heterotic String -- 6.4.4 Vertex Operator Representations -- 6.4.5 Formulas for the Cocycles -- 6.4.6 The Full Current Algebra -- 6.4.7 The Eg and spin(32)/Z2 Lattices -- 6.4.8 The Heterotic String Spectrum -- 6.5 Summary -- Appendix 6. A Elements of E8 -- Appendix 6.B Modular Forms -- 7. Tree Amplitudes -- 7.1 Bosonic Open Strings -- 7.1.1 The Structure of Tree Amplitudes -- 7.1.2 Decoupling of Ghosts -- 7.1.3 Cyclic Symmetry -- 7.1.4 Examples -- 7.1.5 Tree-Level Gauge Invariance -- 7.1.6 The Twist Operator -- 7.2 Bosonic Closed Strings -- 7.2.1 Construction of Tree Amplitudes -- 7.2.2 Examples -- 7.3 Superstrings in the RNS Formulation -- 7.3.1 Open-String Tree Amplitudes in the Bosonic Sector -- 7.3.2 The Fi Picture -- 7.3.3 Examples -- 7.3.4 Tree Amplitudes with One Fermion Line -- 7.3.5 Fermion-Emission Vertices -- 7.4 Superstrings in the Supersymmetric Formulation -- 7.4.1 Massless Particle Vertices -- 7.4.2 Open-String Trees -- 74.3 Closed-String Trees -- 7.4.4 Heterotic String Trees -- 7.5 Summary -- Appendix 7.A Coherent-StateMethods and Correlation Functions -- Bibliography -- Chapter 1 -- Chapter 2 -- Chapter 3 -- Chapter 4 -- Chapter 5 -- Chapter 6. , Chapter 7 -- REFERENCES -- Index.

Note: Cover -- Superstring Theory: Volume 2: Loop Amplitudes, Anomalies and Phenomenology 25th Anniversary Edition -- Dedication -- Title -- Copyright -- Contents -- Preface to the 25th Anniversary Edition -- 8. One-Loop Diagrams in the Bosonic String Theory -- 8.1 Open-String One-Loop Amplitudes -- 8.1.1 The Planar Diagrams -- 8.1.2 The Nonorientable Diagrams -- 8.1.3 Nonplanar Loop Diagrams -- 8.2 Closed-String One-Loop Amplitudes -- 8.2.1 The Torus -- 8.2.2 Modular Invariance -- 8.2.3 The Integration Region -- 8.2.4 Analysis of Divergences -- 8.2.5 The Cosmological Constant -- 8.2.6 Amplitudes with Closed-String Massless States -- 8.3 Other Diagrams for Unoriented Strings -- 8.3.1 Higher-Order Tree Diagrams -- 8.3.2 The Real Projective Plane -- 8.3.3 Other Loop Diagrams -- 8.4 Summary -- Appendix 8.A Jacobi Θ Functions -- 9. One-Loop Diagrams in Superstring Theory -- 9.1 Open-Superstring Amplitudes -- 9.1.1 Amplitudes with M < -- 4 Massless External States -- 9.1.2 The Planar Diagrams -- 9.1.3 Nonorientable Diagrams -- 9.1.4 Orientable Nonplanar Diagrams -- 9.2 Type II Theories -- 9.2.1 Finiteness of the Torus Amplitude -- 9.2.2 Compactification on a Torus -- 9.2.3 The Low-Energy Limit of One-Loop Amplitudes -- 9.3 The Heterotic String Theory -- 9.3.1 The Torus with Four External Particles -- 9.3.2 Modular Invariance of the E% x Es and 50(32) Theories -- 9.4 Calculations in the RNS Formalism -- 9.4.1 Modular Invariance and the GSO Projection -- 9.4.2 The Loop Calculations -- 9.5 Orbifolds and Twisted Strings -- 9.5.1 Generalization of the GSO Projection -- 9.5.2 Strings on Orbifolds -- 9.5.3 Twisted Strings in Ten Dimensions -- 9.5.4 Alternative View Of The SO(16) x SO(16) Theory -- 9.6 Summary -- Appendix 9.A Traces of Fermionic Zero Modes -- Appendix 9.B Modular Invariance of the Functions F2 and C. , 10. The Gauge Anomaly in Type I Superstring Theory -- 10.1 Introduction to Anomalies -- 10.1.1 Anomalies in Point-Particle Field Theory -- 10.1.2 The Gauge Anomaly in D = 10 Super Yang-Mills Theory -- 10.1.3 Anomalies in Superstring Theory -- 10.2 Analysis of Hexagon Diagrams -- 10.2.1 The Planar Diagram Anomaly -- 10.2.2 The Anomaly in the Nonorientable Diagram -- 10.2.3 Absence of Anomalies in Nonplanar Diagrams -- 10.3 Other One-Loop Anomalies in Superstring Theory -- 10.4 Cancellation of Divergences for 50(32) -- 10.4.1 Dilaton Tadpoles and Loop Divergences -- 10.4.2 Divergence Cancellations -- 10.5 Summary -- Appendix 10.A An Alternative Regulator -- 11. Functional Methods in the Light-Cone Gauge -- 11.1 The String Path Integral -- 11.1.1 The Analog Model -- 11.1.2 The Free String Propagator -- 11.1.3 A Lattice Cutoff -- 11.1.4 The Continuum Limit -- 11.2 Amplitude Calculations -- 11.2.1 Interaction Vertices -- 11.2.2 Parametrization of Scattering Processes -- 11.2.3 Evaluation of the Functional Integral -- 11.2.4 Amplitudes with External Ground States -- 11.3 Open-String Tree Amplitudes -- 11.3.1 The Conformal Mapping -- 11.3.2 Evaluation of Amplitudes -- 11.4 Open-String Trees with Excited External States -- 11.4.1 The Green Function on an Infinite Strip -- 11.4.2 Green Functions for Arbitrary Tree Amplitudes -- 11.4.3 The Amplitude in Terms of Oscillators -- 11.4.4 The General Form of the Neumann Coefficients -- 11.4.5 The Neumann Coefficients for the Cubic Open-String Vertex -- 11.5 One-Loop Open-String Amplitudes -- 11.5.1 The Conformal Mapping for the Planar Loop Diagram -- 11.5.2 The Green Function -- 11.5.3 The Planar One-Loop Amplitude -- 11.5.4 Other One-Loop Amplitudes -- 11.6 Closed-String Amplitudes -- 11.6.1 Tree Amplitudes -- 11.6.2 Closed-String One-Loop Amplitudes -- 11.7 Superstrings -- 11.7.1 The SU(4) x U(1) Formalism. , 11.1.2 The Super-Poincaré Generators -- 11.7.3 Supersymmetry Algebra in the Interacting Theory -- 11.7.4 The Continuity Delta Functional -- 11.7.5 Singular Operators Near the Interaction Point -- 11.7.6 The Interaction Terms -- 11.7.7 Tree Amplitudes for Open Superstrings -- 11.8 Summary -- Appendix 11. A The Determinant of the Laplacian -- Appendix 11.B The Jacobian for the Conformal Transformation -- Appendix 11.C Properties of the Functions fm -- Appendix 11. D Properties of the SU(4) Clebsch-Gordan Coefficients -- 12. Some Differential Geometry -- 12.1 Spinors In General Relativity -- 12.2 Spin Structures On The String World Sheet -- 12.3 Topologically Nontrivial Gauge Fields -- 12.3.1 The Tangent Bundle -- 12.3.2 Gauge Fields and Vector Bundles -- 12.4 Differential Forms -- 12.5 Characteristic Classes -- 12.5.1 The Nonabelian Case -- 12.5.2 Characteristic Classes of Manifolds -- 12.5.3 The Euler Characteristic of a Riemann Surface -- 13. Low-Energy Effective Action -- 13.1 Minimal Supergravity Plus Super Yang-Mills -- 13.1.1 N = 1 Supergravity in Ten and Eleven Dimensions -- 13.1.2 Type IIB Supergravity -- 13.1.3 The Coupled Supergravity Super Yang-Mills System -- 13.2 Scale Invariance of the Classical Theory -- 13.3 Anomaly Analysis -- 13.3.1. Structure of Field Theory Anomalies -- 13.3.2 Gravitational Anomalies -- 13.3.3 Mixed Anomalies -- 13.3.4 The Anomalous Feynman Diagrams -- 13.3.5 Mathematical Characterization of Anomalies -- 13.3.6 Other Types of Anomalies -- 13.4 Explicit Formulas for the Anomalies -- 13.5 Anomaly Cancellations -- 13.5.1 Type I Supergravity Without Matter -- 13.5.2 Type IIB Supergravity -- 13.5.3 Allowed Gauge Groups for N = 1 Superstring Theories -- 13.5.4 The SO(16) x SO(16) Theory -- 14. Compactification Of Higher Dimensions -- 14.1 Wave Operators in Ten Dimensions -- 14.1.1 Massless Fields in Ten Dimensions. , 14.1.2 Zero Modes of Wave Operators -- 14.2 Massless Fermions -- 14.2.1 The Index of the Dirac Operator -- 14.2.2 Incorporation of Gauge Fields -- 14.2.3 The Chiral Asymmetry -- 14.2.4 The Rarita-Schwinger Operator -- 14.2.5 Outlook -- 14.3 Zero Modes of Antisymmetric Tensor Fields -- 14.3.1 Antisymmetric Tensor Fields -- 14-3.2 Application to Axions in N = 1 Superstring Theory -- 14.3.3 The 'Nonzero Modes' -- 14.3.4 The Exterior Derivative and the Dirac Operator -- 14.4 Index Theorems on the String World Sheet -- 14.4.1 The Dirac Index -- 14.4.2 The Euler Characteristic -- 14.4.3 Zero Modes of Conformal Ghosts -- 14.4.4 Zero Modes of Superconformal Ghosts -- 14.5 Zero Modes of Nonlinear Fields -- 14.6 Models of the Fermion Quantum Numbers -- 14.7 Anomaly Cancellation in Four Dimensions -- 15. Some Algebraic Geometry -- 15.1 Low-Energy Supersymmetry -- 15.1.1 Motivation -- 15.1.2 Conditions for Unbroken Supersymmetry -- 15.1.3 Manifolds of SU(3) Holonomy -- 15.2 Complex Manifolds -- 15.2.1 Almost Complex Structure -- 15.2.2 The Nijenhuis Tensor -- 15.2.3 Examples of Complex Manifolds -- 15.3 Kahler Manifolds -- 15.3.1 The Kahler Metric -- 15.3.2 Exterior Derivatives -- 15.3.3 The Affine Connection and the Riemann Tensor -- 15.3.4 Examples of Kahler Manifolds -- 15.4 Ricci-Flat Kahler Manifolds and SU(N) Holonomy -- 15.4.1 The Calabi-Yau Metric -- 15.4.2 Covariantly Constant Forms -- 15.4.3 Some Manifolds of SU(N) Holonomy -- 15.5 Wave Operators on Kahler Manifolds -- 15.5.1 The Dirac Operator -- 15.5.2 Dolbeault Cohomology -- 15.5.3 The Hodge Decomposition -- 15.5.4 Hodge Numbers -- 15.6 Yang-Mills Equations and Holomorphic Vector Bundles -- 15.6.1 Holomorphic Vector Bundles -- 15.6.2 The Donaldson-Uhlenbeck-Yau Equation -- 15.6.3 Examples -- 15.7 Dolbeault Cohomology and Some Applications -- 15.7.1 Zero Modes of the Dirac Operator. , 15.7.2 Deformations of Complex Manifolds -- 15.7.3 Deformations of Holomorphic Vector Bundles -- 15.8 Branched Coverings of Complex Manifolds -- 16. Models of Low-Energy Supersymmetry -- 16.1 A Simple Ansatz -- 16.2 The Spectrum of Massless Particles -- 16.2.1 Zero Modes of Charged Fields -- 16.2.2 Fluctuations of the Gravitational Field -- 16.2.3 The Other Bose Fields -- 16.3 Symmetry Breaking by Wilson Lines -- 16.3.1 Symmetry Breaking Patterns -- 16.3.2 A Four Generation Model -- 16.4 Relation to Conventional Grand Unification -- 16.4.1 Alternative Description of Symmetry Breaking -- 16.4.2 E6 Relations among Coupling Constants -- 16.4.3 Counting Massless Particles -- 16.4.4 Fractional Electric Charges -- 16.4.5 Discussion -- 16.5 Global Symmetries -- 16.5.1 CP Conservation in Superstring Models -- 16.5.2 R Transformations in Superstring Models -- 16.5.3 Global Symmetries of the Toy Model -- 16.5.4 Transformation Laws of Matter Fields -- 16.6 Topological Formulas for Yukawa Couplings -- 16.6.1 A Topological Formula for the Superpotential -- 16.6.2 The Kinetic Terms -- 16.6.3 A Nonrenormalization Theorem and Its Consequences -- 16.6.4 Application to the Toy Model -- 16.7 Another Approach to Symmetry Breaking -- 16.8 Discussion -- 16.9 Renormalization of Coupling Constants -- 16.10 Orbifolds and Algebraic Geometry -- 16.11 Outlook -- Bibliography -- Chapter 8 -- Chapter 9 -- Chapter 10 -- Chapter 11 -- Chapter 12 -- Chapter 13 -- Chapter 14 -- Chapter 15 -- Chapter 16 -- REFERENCES -- String Field Theory -- REFERENCES -- Index.