Scattering amplitudes: the most perfect microscopic structures in the universe

Abstract

This article gives an overview of many of the recent developments in understanding the structure of relativistic scattering amplitudes in gauge theories ranging from QCD to N=4 super-Yang-Mills theory, as well as (super)gravity. I also provide a pedagogical introduction to some of the basic tools used to organize and illuminate the color and kinematic structure of amplitudes. This article is an invited review introducing a special issue of Journal of Physics A devoted to "Scattering Amplitudes in Gauge Theories".

29 pages, 8 figures. v2: references added, typos fixed

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• New Relations for Gauge-Theory Amplitudes
• Gluon scattering amplitudes at strong coupling
• Reducing full one-loop amplitudes to scalar integrals at the integrand level
• Classical Polylogarithms for Amplitudes and Wilson Loops
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• An Automated Implementation of On-Shell Methods for One-Loop Amplitudes
• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
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• The Complete Planar S-matrix of N=4 SYM as a Wilson Loop in Twistor Space
• A Numerical Unitarity Formalism for Evaluating One-Loop Amplitudes
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• An Operator Product Expansion for Polygonal null Wilson Loops
• The hexagon Wilson loop and the BDS ansatz for the six-gluon amplitude
• BFKL Pomeron, Reggeized gluons and Bern-Dixon-Smirnov amplitudes
• All tree-level amplitudes in N=4 SYM
• Basics of Generalized Unitarity
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• Tree-Level Formalism
• Exact Superconformal and Yangian Symmetry of Scattering Amplitudes
• SUSY Ward identities, Superamplitudes, and Counterterms
• On Cancellations of Ultraviolet Divergences in Supergravity Amplitudes
• Integrable spin chains and scattering amplitudes
• Tree-level amplitudes and dual superconformal symmetry
• One-loop N = 4 super Yang-Mills scattering amplitudes in d dimensions, relation to open strings and polygonal Wilson loops

Cited by in corpus (57)

• QCD and strongly coupled gauge theories: challenges and perspectives
• Classical black hole scattering from a worldline quantum field theory
• Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes
• Five-Point Amplitudes in N=4 Super-Yang-Mills Theory and N=8 Supergravity
• Motivic Multiple Zeta Values and Superstring Amplitudes
• Color-Kinematics Duality for Pure Yang-Mills and Gravity at One and Two Loops
• Color-kinematic Duality for Form Factors
• Basics of Generalized Unitarity
• The Structure of n-Point One-Loop Open Superstring Amplitudes
• D = 5 maximally supersymmetric Yang-Mills theory diverges at six loops
• Simple superamplitudes in higher dimensions
• Integrand Reduction for Two-Loop Scattering Amplitudes through Multivariate Polynomial Division
• The Five-Loop Four-Point Amplitude of N=4 super-Yang-Mills Theory
• Spectral Parameters for Scattering Amplitudes in N=4 Super Yang-Mills Theory
• An Introduction to On-shell Recursion Relations
• Transverse-momentum spectra of electroweak bosons near threshold at NNLO
• New relations for scattering amplitudes in Yang-Mills theory at loop level
• The Multi-Regge limit of NMHV Amplitudes in N=4 SYM Theory
• New structures in scattering amplitudes: a review
• Evaluating the 6-point Remainder Function Near the Collinear Limit
• Complete N-Point Superstring Disk Amplitude II. Amplitude and Hypergeometric Function Structure
• Maximal R-symmetry violating amplitudes in type IIB superstring theory
• Note on asymptotic symmetries and soft gluon theorems
• Exact Superconformal and Yangian Symmetry of Scattering Amplitudes
• A new integral formula for supersymmetric scattering amplitudes in three dimensions
• The structure of IR divergences in celestial gluon amplitudes
• Soft theorems in maximally supersymmetric theories
• OPE for Super Loops
• On DIS Wilson coefficients in N = 4 super Yang-Mills theory
• The SAGEX Review on Scattering Amplitudes, Chapter 7: Positive Geometry of Scattering Amplitudes
• String-inspired representations of photon/gluon amplitudes
• Twistor actions for gauge theory and gravity
• Perturbative linearization of super-Yang-Mills theories in general gauges
• Symbols of One-Loop Integrals From Mixed Tate Motives
• Coordinate-space singularities of massless gauge theories
• The property of maximal transcendentality: calculation of master integrals
• Four Loop Scattering in the Nambu-Goto Theory
• The property of maximal transcendentality: calculation of Feynman integrals
• Color structures and permutations
• Tree-level amplitudes and dual superconformal symmetry
• The SAGEX Review on Scattering Amplitudes, Chapter 5: Analytic Bootstraps for Scattering Amplitudes and Beyond
• On the singlet projector and the monodromy relation for psu(2, 2|4) spin chains and reduction to subsectors
• Kleiss-Kuijf Relations from Momentum Amplituhedron Geometry
• Applications of Subleading-color Amplitudes in N=4 SYM Theory
• Permutation Relations of Yangian Invariants, Unitarity Cuts, and Scattering Amplitudes
• Helicity Amplitudes for massive gravitinos in N=1 Supergravity
• Transmutation operators and expansions for $1$-loop Feynman integrands
• The Steinmann Cluster Bootstrap for N=4 Super Yang-Mills Amplitudes
• Quantum Effects for Black Holes with On-Shell Amplitudes
• Perturbative gauge theory and 2+2=4
• Nonplanar On-shell Diagrams and Leading Singularities of Scattering Amplitudes
• Perturbative Gravity and Gauge Theory Relations -- A Review
• Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes
• Gauge theory one-loop amplitudes and the BCFW recursion relations
• 1-loop Color structures and sunny diagrams
• Scattering Amplitudes in Gauge Theories
• Partial fractioning reduction of perturbative amplitudes