Scattering Amplitudes in Gauge Theory and Gravity

Höfundar: Henriette Elvang; Yu-tin Huang (Útgáfa: 1)
Scattering Amplitudes in Gauge Theory and Gravity

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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.

Nánar um bókina

Útgefandi
Cambridge University Press
ISBN
9781316189580
Print ISBN
9781107069251
Format
ePub
Útgáfa
1
Höfundar
Henriette Elvang; Yu-tin Huang
Tungumál
English
Útgefið
2015-02-05
Prent takmörkun á líftíma
10
Prent takmörkun
5
Afritunar takmörkun
5

Kaflar

  • Cover
  • Half title
  • Title
  • Copyright
  • Dedication
  • Table of Contents
  • Preface
  • 1 Introduction
  • Part I Trees
  • 2 Spinor helicity formalism
  • 2.1 Dirac spinors
  • 2.2 Spinor helicity notation
  • 2.3 Examples from Yukawa theory
  • 2.4 Massless vectors and examples from QED
  • 2.5 Yang–Mills theory, QCD, and color-ordering
  • 2.6 Little group scaling
  • 2.7 MHV classification
  • 2.8 Analytic properties of tree amplitudes
  • 3 On-shell recursion relations at tree-level
  • 3.1 Complex shifts and Cauchy’s theorem
  • 3.2 BCFW recursion relations
  • 3.3 When does it work?
  • 3.4 MHV vertex expansion (CSW)
  • 4 Supersymmetry
  • 4.1 N = 1 supersymmetry: chiral model
  • 4.2 Amplitudes and supersymmetry Ward identities
  • 4.3 N = 1 supersymmetry: gauge theory
  • 4.4 N = 4 SYM: on-shell superspace and superamplitudes
  • 4.5 Super-BCFW and all tree-level amplitudes in N = 4 SYM
  • 4.5.1 MHV superamplitude from super-BCFW
  • 4.5.2 NMHV superamplitude and beyond
  • 5 Symmetries of N = 4 SYM
  • 5.1 Superconformal symmetry of N = 4 SYM
  • 5.2 Twistors
  • 5.3 Emergence of dual conformal symmetry
  • 5.4 Momentum twistors
  • Part II Loops
  • 6 Loop amplitudes and generalized unitarity
  • 6.1 UV and IR divergences
  • 6.2 Unitarity method
  • 6.3 1-loop amplitudes from unitarity
  • 6.4 1-loop amplitudes in planar N = 4 SYM
  • 6.5 Higher-loop amplitudes in planar N = 5 SYM
  • 7 BCFW recursion for loops
  • 7.1 Loop-integrands
  • 7.2 BCFW shift in momentum twistor space
  • 7.3 Momentum twistor BCFW at tree-level
  • 7.4 Momentum twistor BCFW for planar loop-integrands
  • 7.5 Example: 4-point 1-loop amplitude from recursion
  • 7.6 Higher loops
  • 8 Leading Singularities and on-shell diagrams
  • 8.1 1-loop Leading Singularities
  • 8.2 2-loop Leading Singularities
  • 8.3 On-shell diagrams
  • Part III Topics
  • 9 Grassmannia
  • 9.1 Yangian invariance and cyclic symmetry
  • 9.2 The Grassmannian
  • 9.3 Yangian invariants as residues in the Grassmannian
  • 9.3.1 MHV amplitudes
  • 9.3.2 6-point NMHV amplitudes
  • 9.4 From on-shell diagrams to the Grassmannian
  • 10 Polytopes
  • 10.1 Volume of an n-simplex in CP[sup(n)]
  • 10.2 NMHV tree superamplitude as the volume of a polytope
  • 10.3 The boundary of simplices and polytopes
  • 10.4 Geometric aftermath
  • 11 Amplitudes in dimensions D ≠ 4
  • 11.1 Helicity formalism in D ≠ 4
  • 11.2 Scattering amplitudes in D = 6
  • 11.3 Scattering amplitudes in D = 3
  • 11.3.1 D = 3 kinematics
  • 11.3.2 3d SYM and Chern–Simons theory
  • 11.3.3 Special kinematics and poles in amplitudes
  • 11.3.4 D = 3 superconformal algebra
  • 11.3.5 N = 8 superconformal theory: BLG
  • 11.3.6 N = 6 superconformal theory: ABJM
  • 11.3.7 BCFW recursion in 3d
  • 11.3.8 ABJM and dual conformal symmetry
  • 11.3.9 Loops and on-shell diagrams in ABJM
  • 11.3.10 The orthogonal Grassmannian
  • 12 Supergravity amplitudes
  • 12.1 Perturbative gravity
  • 12.2 Supergravity
  • 12.3 Superamplitudes in N = 8 supergravity
  • 12.4 Loop amplitudes in supergravity
  • 12.5 N = 8 supergravity: loops and counterterms
  • 12.6 Supergravity divergences for various N, L, and D
  • 13 A colorful duality
  • 13.1 The color-structure of Yang–Mills theory
  • 13.2 Color-kinematics duality: BCJ, the tree-level story
  • 13.3 Color-kinematics duality: BCJ, the loop-level story
  • 13.3.1 1-loop 4-point N = 4 SYM
  • 13.3.2 2-loop 4-point N = 4 SYM
  • 13.3.3 3-loop 4-point N = 4 SYM
  • 13.3.4 Summary
  • 13.4 Implications for UV behavior of supergravity
  • 13.5 Extensions
  • 14 Further reading
  • Appendix Conventions for 4d spinor helicity formalism
  • References
  • Index