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1 Introduction and Basics |
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1 | (34) |
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1.1 Lorentz and Poincare Group, Algebra and Representations |
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1 | (2) |
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1.2 Weyl and Dirac Spinors |
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3 | (3) |
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1.3 Non-Abelian Gauge Theories |
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6 | (4) |
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1.4 Scattering Amplitudes and Feynman Rules for Gauge Theories |
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10 | (4) |
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1.5 Massless Particles: Helicity |
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14 | (1) |
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1.6 Spinor Helicity Formalism for Massless Particles |
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15 | (3) |
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18 | (1) |
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1.8 Fermion Polarizations |
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19 | (1) |
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20 | (4) |
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1.10 Color Ordered Feynman Rules and Properties of Color-Ordered Amplitudes |
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24 | (3) |
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1.11 Vanishing Tree Amplitudes |
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27 | (2) |
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1.12 The Four-Gluon Tree-Amplitude |
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29 | (3) |
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1.13 References and Further Reading |
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32 | (3) |
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32 | (3) |
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35 | (46) |
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2.1 Britto-Cachazo-Feng-Witten (BCFW) On-shell Recursion |
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35 | (7) |
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2.2 The Gluon Three-Point Amplitude |
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42 | (1) |
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2.3 An Example: MHV Amplitudes |
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43 | (2) |
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2.4 Factorization Properties of Tree-Level Amplitudes |
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45 | (5) |
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2.4.1 Factorization on Multi-Particle Poles |
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46 | (1) |
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2.4.2 Absence of Multi-Particle Poles in MHV Amplitudes |
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46 | (1) |
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46 | (2) |
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48 | (2) |
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2.5 On-shell Recursion for Amplitudes with Massive Particles |
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50 | (5) |
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2.6 Poincare and Conformal Symmetry |
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55 | (4) |
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2.7 N = 4 Super Yang-Mills Theory |
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59 | (19) |
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2.7.1 On-shell Superspace and Superfields |
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61 | (2) |
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2.7.2 Superconformal Symmetry |
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63 | (2) |
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2.7.3 Super-amplitudes, and Extraction of Components |
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65 | (3) |
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2.7.4 Super BCFW-Recursion |
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68 | (2) |
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2.7.5 Three-Point Super-amplitudes |
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70 | (1) |
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2.7.6 Solving the Super-BCFW Recursion: MHV Case |
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71 | (3) |
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2.7.7 Solving the Super-BCFW Recursion: NMHV Case |
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74 | (4) |
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2.8 References and Further Reading |
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78 | (3) |
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79 | (2) |
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81 | (66) |
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81 | (1) |
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3.2 Conventions for Minkowski-Space Integrals |
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82 | (2) |
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3.3 General Remarks, Ultraviolet and Infrared Divergences |
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84 | (4) |
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3.3.1 Ultraviolet Divergences |
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86 | (1) |
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3.3.2 Infrared Divergences |
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86 | (1) |
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3.3.3 Regularization Scheme |
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87 | (1) |
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88 | (14) |
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3.4.1 The Van Neerven-Vermaseren Basis |
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90 | (2) |
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3.4.2 Reduction of the Integrand in D = 4 - 2ε Dimensions |
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92 | (5) |
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3.4.3 Higher Dimensional Loop Momentum Integration |
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97 | (2) |
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3.4.4 An Example: The Photon Self-Energy in Massless QED |
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99 | (3) |
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102 | (25) |
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3.5.1 Two-Particle Cuts of the Four Gluon Amplitude |
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103 | (9) |
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3.5.2 Generalized Unitarity and Higher-Order Cuts |
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112 | (9) |
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3.5.3 Rational Part: All-Plus Helicity Amplitudes |
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121 | (2) |
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3.5.4 An Example: Higgs Production via Gluon Fusion |
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123 | (4) |
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3.6 Overview of Integration Techniques for Loop Integrals |
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127 | (4) |
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3.6.1 Notation and Dual Coordinates |
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128 | (1) |
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3.6.2 Feynman Parametrization |
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129 | (2) |
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3.7 Mellin-Barnes Techniques |
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131 | (5) |
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3.7.1 Resolution of Singularities in ε |
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133 | (1) |
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3.7.2 Asymptotic Expansions and Resummation |
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134 | (1) |
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3.7.3 Numerical Evaluation and Convergence |
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135 | (1) |
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3.8 Integration by Parts and Differential Equations |
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136 | (5) |
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3.8.1 Integration by Parts Identities |
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136 | (1) |
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3.8.2 Differential Equations |
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137 | (2) |
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3.8.3 Simplified Approach to Differential Equations |
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139 | (2) |
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3.9 References and Further Reading |
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141 | (6) |
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143 | (4) |
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147 | (24) |
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4.1 Recursion Relations for Loop Integrands |
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147 | (5) |
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4.2 Scattering Amplitudes in N = 4 Super Yang-Mills |
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152 | (1) |
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4.3 Wilson Loop/Scattering Amplitude Duality |
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153 | (5) |
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4.4 (Dual) Conformal Symmetry |
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158 | (4) |
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4.4.1 Conformal Ward Identities for Cusped Wilson Loops |
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158 | (2) |
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4.4.2 Dual Conformal Symmetry of Scattering Amplitudes |
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160 | (2) |
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4.5 Dual Superconformal and Yangian Symmetry |
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162 | (3) |
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4.6 From Correlation Functions to Wilson Loops and Scattering Amplitudes |
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165 | (2) |
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4.7 References and Further Reading |
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167 | (4) |
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167 | (4) |
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Appendix A Renormalization Properties of Wilson Loops |
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171 | (4) |
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173 | (2) |
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Appendix B Conventions and Useful Formulae |
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175 | |
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Solutions to the Exercises |
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177 | |
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195 | |