Scattering Amplitudes in Gauge Theory and Gravity

Henriette Elvang; Yu-tin Huang

doi:10.1017/CBO9781107706620

Providing a comprehensive, pedagogical introduction to scattering amplitudes in gauge theory and gravity, this book is ideal for graduate students and researchers. It offers a smooth transition from basic quantum field theory to the frontier of modern research. The book starts with an introduction to the spinor helicity formalism in the context of Feynman rules for tree-level amplitudes. The material covered includes on-shell recursion relations, superamplitudes, symmetries of N=4 super Yang–Mills theory, twistors and momentum twistors, Grassmannians, and polytopes. The presentation also covers amplitudes in perturbative supergravity, 3D Chern–Simons matter theories, and color–kinematics duality and its connection to 'gravity=(gauge theory)x(gauge theory)'. Basic knowledge of Feynman rules in scalar field theory and quantum electrodynamics is assumed, but all other tools are introduced as needed. Worked examples and more than 150 exercises are included. This title is also available as open access on Cambridge Core.

‘In recent years, a series of surprising insights and new methods have transformed the understanding of gauge and gravitational scattering amplitudes. These advances are important both for practical calculations in particle physics, and for the fundamental structure of relativistic quantum theory. Elvang and Huang have written the first comprehensive text on this subject, and their clear and pedagogical approach will make these new ideas accessible to a wide range of students.’

Joseph Polchinski - University of California, Santa Barbara

‘This book provides a much-needed text covering modern techniques that have given radical new insights into the structure of quantum field theory. It gathers together a very large body of recent literature and presents it in a coherent style. The book should appeal to the wide body of researchers who wish to use quantum field theory as a tool for describing physical phenomena or who are intending to gain insight by studying its mathematical structure.’

Michael B. Green - University of Cambridge

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Contents

Frontmatter
pp i-iv
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Dedication
pp v-v
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Other
pp vi-vi
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Contents
pp vii-x
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Preface
pp xi-xii
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1 - Introduction
pp 1-12
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Part I - Trees
pp 13-14
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2 - Spinor helicity formalism
pp 15-49
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3 - On-shell recursion relations at tree-level
pp 50-68
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4 - Supersymmetry
pp 69-94
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5 - Symmetries of 𝒩 = 4 SYM
pp 95-114
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Part II - Loops
pp 115-116
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6 - Loop amplitudes and generalized unitarity
pp 117-137
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7 - BCFW recursion for loops
pp 138-160
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8 - Leading Singularities and on-shell diagrams
pp 161-178
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Part III - Topics
pp 179-180
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9 - Grassmannia
pp 181-199
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10 - Polytopes
pp 200-215
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11 - Amplitudes in dimensions D ≠ 4
pp 216-248
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12 - Supergravity amplitudes
pp 249-271
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13 - A colorful duality
pp 272-293
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14 - Further reading
pp 294-296
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Appendix - Conventions for 4d spinor helicity formalism
pp 297-298
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References
pp 299-318
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Index
pp 319-323
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Scattering Amplitudes in Gauge Theory and Gravity

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Contents

Frontmatter
pp i-iv

Dedication
pp v-v

Other
pp vi-vi

Contents
pp vii-x

Preface
pp xi-xii

1 - Introduction
pp 1-12

Part I - Trees
pp 13-14

2 - Spinor helicity formalism
pp 15-49

3 - On-shell recursion relations at tree-level
pp 50-68

4 - Supersymmetry
pp 69-94

5 - Symmetries of 𝒩 = 4 SYM
pp 95-114

Part II - Loops
pp 115-116

6 - Loop amplitudes and generalized unitarity
pp 117-137

7 - BCFW recursion for loops
pp 138-160

8 - Leading Singularities and on-shell diagrams
pp 161-178

Part III - Topics
pp 179-180

9 - Grassmannia
pp 181-199

10 - Polytopes
pp 200-215

11 - Amplitudes in dimensions D ≠ 4
pp 216-248

12 - Supergravity amplitudes
pp 249-271

13 - A colorful duality
pp 272-293

14 - Further reading
pp 294-296

Appendix - Conventions for 4d spinor helicity formalism
pp 297-298

References
pp 299-318

Index
pp 319-323

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Scattering Amplitudes in Gauge Theory and Gravity

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