Scattering Amplitudes

Abstract

The purpose of this review is to bridge the gap between a standard course in quantum field theory and recent fascinating developments in the studies of on-shell scattering amplitudes. We build up the subject from basic quantum field theory, starting with Feynman rules for simple processes in Yukawa theory and QED. The material covered includes spinor helicity formalism, on-shell recursion relations, superamplitudes and their symmetries, twistors and momentum twistors, loops and integrands, Grassmannians, polytopes, and amplitudes in perturbative supergravity as well as 3d Chern-Simons-matter theories. Multiple examples and exercises are included.

269 pages, 134 figures. v2: Typos corrected. This is part of textbook to be published by Cambridge University Press

References in corpus (24)

• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• Algebraic structures on parallel M2-branes
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• Minimal Basis for Gauge Theory Amplitudes
• The Complete Planar S-matrix of N=4 SYM as a Wilson Loop in Twistor Space
• Gauge Amplitude Identities by On-shell Recursion Relation in S-matrix Program
• Space-time S-matrix and Flux tube S-matrix II. Extracting and Matching Data
• The Ultraviolet Properties of N=4 Supergravity at Four Loops
• Studies of the ABJM Theory in a Formulation with Manifest SU(4) R-Symmetry
• Ultraviolet properties of Maximal Supergravity
• The Yangian origin of the Grassmannian integral
• Yangian Invariant Scattering Amplitudes in Supersymmetric Chern-Simons Theory
• Stringy KLT relations, global symmetries, and E_7(7) violation
• Spinor Helicity and Dual Conformal Symmetry in Ten Dimensions
• Dual Conformal Properties of Six-Dimensional Maximal Super Yang-Mills Amplitudes
• Decoupling Supergravity from the Superstring
• MHV Diagrams in Momentum Twistor Space
• Conformal Anomaly for Amplitudes in N=6 Superconformal Chern-Simons Theory
• A simple formula for gravitational MHV amplitudes
• One Loop Amplitudes In ABJM
• N=8 Counterterms and E7(7) Current Conservation
• Recursion Relations for Tree-level Amplitudes in the SU(N) Non-linear Sigma Model
• Complete Six-Gluon Disk Amplitude in Superstring Theory
• Amplitudes at Weak Coupling as Polytopes in AdS_5

Cited by in corpus (71)

• Evidence for a New Soft Graviton Theorem
• Lectures on Celestial Amplitudes
• Helicity Selection Rules and Non-Interference for BSM Amplitudes
• Black Hole Formation and Classicalization in Ultra-Planckian 2 -> N Scattering
• The Cosmic Galois Group and Extended Steinmann Relations for Planar $\mathcal{N}=4$ SYM Amplitudes
• Closed Superstring Amplitudes, Single-Valued Multiple Zeta Values and Deligne Associator
• Towards one-loop SYM amplitudes from the pure spinor BRST cohomology
• The Inflationary Wavefunction from Analyticity and Factorization
• On duality of color and kinematics in (A)dS momentum space
• $(2,2)$ Scattering and the Celestial Torus
• Einstein-Yang-Mills from pure Yang-Mills amplitudes
• Effective Field Theory of Gravity to All Orders
• Shifting Spin on the Celestial Sphere
• Covariant Color-Kinematics Duality
• Twin Supergravities from Yang-Mills Squared
• Cutting through form factors and cross sections of non-protected operators in N=4 SYM
• On-shell Diagrams, Graßmannians and Integrability for Form Factors
• Massive Higher Spins: Effective Theory and Consistency
• Fermionic pentagons and NMHV hexagon
• Residual Local Supersymmetry and the Soft Gravitino
• Double Field Theory as the Double Copy of Yang-Mills
• Scattering Amplitudes in Quantum Field Theory
• On loop celestial amplitudes for gauge theory and gravity
• Gravitational Causality and the Self-Stress of Photons
• Unitarization from Geometry
• Ultraviolet divergences and factorization for coordinate-space amplitudes
• All-Multiplicity Non-Planar MHV Amplitudes in sYM at Two Loops
• Towards Color-Kinematics Duality in Generic Spacetimes
• Dispersion Formulas in QFTs, CFTs, and Holography
• Minimally modified theories of gravity: a playground for testing the uniqueness of general relativity
• Spinor-helicity and the algebraic classification of higher-dimensional spacetimes
• Conformally Soft Fermions
• The quark induced Mueller-Tang jet impact factor at next-to-leading order
• On the Supersymmetrization of Galileon Theories in Four Dimensions
• RG Equations and High Energy Behaviour in Non-Renormalizable Theories
• Chiral Squaring
• Four dimensional ambitwistor strings and form factors of local and Wilson line operators
• Multi-soft theorems in Gauge Theory from MHV Diagrams
• Note on the asymptotic structure of Kerr-Schild form
• Bootstrap and Amplitudes: A Hike in the Landscape of Quantum Field Theory
• Four Loop Scattering in the Nambu-Goto Theory
• Challenges of D=6 N=(1,1) SYM Theory
• Kinematically Dependent Renormalization
• On Multi-step BCFW Recursion Relations
• The four-loop six-gluon NMHV ratio function
• CP and other Symmetries of Symmetries
• Gauging the superconformal group with a graded dual operator
• Dilaton Effective Action with $\mathcal{N}=1$ Supersymmetry
• The Information Metric on the moduli space of instantons with global symmetries
• Some tree-level string amplitudes in the NSR formalism
• Amplitudes in fishnet theories in diverse dimensions and Box ladder diagrams
• Learning the Simplicity of Scattering Amplitudes
• Collinearity constraints for on-shell massless particle three-point functions, and implications for allowed-forbidden $n+1$-point functions
• Directed graphs and interferometry
• Perturbative gauge theory and 2+2=4
• On hydrogen-like bound states in $\mathcal{N}=4$ super Yang-Mills
• Ambitwistor strings and reggeon amplitudes in N=4 SYM
• Scattering of Stringy States in Compactified Closed Bosonic String
• An SZ-Like Effect on Cosmological Gravitational Wave Backgrounds
• The KLT relations in unimodular gravity
• Application of BCFW-recursion relations and the Feynman-tree theorem to the four gluon amplitude with all plus helicities
• General relativity as a two-dimensional CFT
• Non-Perturbative Four-Point Scattering from First-Quantized Relativistic JWKB
• Embedding of rank two supercharges in the superconformal algebra
• General expressions for extra-dimensional tree amplitudes and all-plus 1-loop integrands in Q-cut representaion
• Dual Conformal Symmetry and Iterative Integrals in Six Dimensions
• Celestial Holography
• Boundary Contributions of On-shell Recursion Relations With Multiple-line Deformation
• Subleading Corrections to Hadronic Cross-Sections at High Energies
• On-shell Methods for Form Factors in N=4 SYM and Their Applications
• Cyclicity of All Anti-NMHV and N${}^2$MHV Tree Amplitudes in N=4 SYM