The Duality Between Color and Kinematics and its Applications

Abstract

This review describes the duality between color and kinematics and its applications, with the aim of gaining a deeper understanding of the perturbative structure of gauge and gravity theories. We emphasize, in particular, applications to loop-level calculations, the broad web of theories linked by the duality and the associated double-copy structure, and the issue of extending the duality and double copy beyond scattering amplitudes. The review is aimed at doctoral students and junior researchers both inside and outside the field of amplitudes and is accompanied by various exercises.

LaTeX, 37 figures, 208 pages

Cited by in corpus (92)

• Advances in QED with intense background fields
• Scattering Amplitudes and Conservative Binary Dynamics at $\mathcal{O}(G^4)$
• Classical Gravitational Bremsstrahlung from a Worldline Quantum Field Theory
• Scattering Amplitudes, the Tail Effect, and Conservative Binary Dynamics at $O(G^4)$
• Conservative Dynamics of Binary Systems at Fourth Post-Minkowskian Order in the Large-eccentricity Expansion
• Gravitational Bremsstrahlung from Reverse Unitarity
• Gravitational Effective Field Theory Islands, Low-Spin Dominance, and the Four-Graviton Amplitude
• Gravitational Bremsstrahlung and Hidden Supersymmetry of Spinning Bodies
• Gravitational Bremsstrahlung in the Post-Minkowskian Effective Field Theory
• Tidal Effects in the Post-Minkowskian Expansion
• Universality in the classical limit of massless gravitational scattering
• The Double Copy of Electric-Magnetic Duality
• On duality of color and kinematics in (A)dS momentum space
• The Weyl Double Copy for Gravitational Waves
• A new gauge-invariant double copy for heavy-mass effective theory
• The two-loop five-point amplitude in $\mathcal{N}=8$ supergravity
• The classical double copy of non-singular black holes
• BRST-Lagrangian Double Copy of Yang-Mills Theory
• Radiated momentum in the Post-Minkowskian worldline approach via reverse unitarity
• Covariant Color-Kinematics Duality
• Double copy structure and the flat space limit of conformal correlators in even dimensions
• Gravitational radiation from inspiralling compact objects: Spin-spin effects completed at the next-to-leading post-Newtonian order
• Kinematic Jacobi Identity is a Residue Theorem: Geometry of Color-Kinematics Duality for Gauge and Gravity Amplitudes
• Ehlers as EM duality in the double copy
• The double copy for heavy particles
• Classical double copy at null infinity
• Simple encoding of higher derivative gauge and gravity counterterms
• Tree-level amplitudes from the pure spinor superstring
• Double Field Theory as the Double Copy of Yang-Mills
• Celestial double copy from the worldsheet
• Constraints on a Massive Double-Copy and Applications to Massive Gravity
• Asymptotic Weyl Double Copy
• One-loop Gluon Amplitudes in AdS
• Composing Effective Prediction at Five Points
• Loop-Level Double-Copy for Massive Quantum Particles
• On loop celestial amplitudes for gauge theory and gravity
• New Soft Theorems for Goldstone Boson Amplitudes
• One-loop Correlators and BCJ Numerators from Forward Limits
• Unitarization from Geometry
• 10D Super-Yang-Mills Scattering Amplitudes From Its Pure Spinor Action
• The double copy of the multipole expansion
• Dispersion Formulas in QFTs, CFTs, and Holography
• Towards Color-Kinematics Duality in Generic Spacetimes
• Graviton scattering in self-dual radiative space-times
• Majorana Neutrinos, Exceptional Jordan Algebra, and Mass Ratios for Charged Fermions
• Non-planar form factors of generic local operators via on-shell unitarity and color-kinematics duality
• Propagators, BCFW Recursion and New Scattering Equations at One Loop
• Algebraic branch points at all loop orders from positive kinematics and wall crossing
• Soft Gravity by Squaring Soft QED on the Celestial Sphere
• Weyl double copy and massless free fields in curved spacetimes
• Exact results for scattering on ultra-short plane wave backgrounds
• Expansion of Einstein-Yang-Mills theory by Differential Operators
• Scattering of Gravitons and Spinning Massive States from Compact Numerators
• Extracting Bigravity from String Theory
• Generalised Schwarzschild metric from double copy of point-like charge solution in Born-Infeld theory
• A Lie bracket for the momentum kernel
• Gauge $\times$ Gauge $=$ Gravity on Homogeneous Spaces using Tensor Convolutions
• Structure of Chern-Simons Scattering Amplitudes from Topological Equivalence Theorem and Double-Copy
• Black Hole Horizons from the Double Copy
• The classical double copy in curved spacetimes: Perturbative Yang-Mills from the bi-adjoint scalar
• Double copy for Lagrangians at trilinear order
• Color-kinematics duality, double copy and the unitarity method for higher-derivative QCD and quadratic gravity
• Manifest colour-kinematics duality and double-copy in the string-based formalism
• One-Loop Yang-Mills Integrands from Scattering Equations
• Scattering Amplitudes of Kaluza-Klein Strings and Extended Massive Double-Copy
• Worldline description of a bi-adjoint scalar and the zeroth copy
• Quantum Corrections to Generic Branes: DBI, NLSM, and More
• Bootstrap and Amplitudes: A Hike in the Landscape of Quantum Field Theory
• The Amplitude for Classical Gravitational Scattering at Third Post-Minkowskian Order
• Note on the asymptotic structure of Kerr-Schild form
• Exploring the Landscape for Soft Theorems of Nonlinear Sigma Models
• A scattering amplitudes approach to hard thermal loops
• Homotopy double copy and the Kawai-Lewellen-Tye relations for the non-abelian and tensor Navier-Stokes equations
• One-loop multicollinear limits from 2-point amplitudes on self-dual backgrounds
• A homotopy BV algebra for Yang-Mills and color-kinematics
• The double copy: from optics to quantum gravity
• Gravitational Equivalence Theorem and Double-Copy for Kaluza-Klein Graviton Scattering Amplitudes
• BCJ, worldsheet quantum algebra and KZ equations
• Next-to-MHV Yang-Mills kinematic algebra
• Infrared and Holographic Aspects of the $S$-Matrix in Gauge Theory and Gravity
• UV consistency conditions for CHY integrands
• Exploration of a Singular Fluid Spacetime
• Two-loop superstring five-point amplitudes I: Construction via chiral splitting and pure spinors
• The origin of the KLT relations and nonlinear relations for Yang-Mills amplitudes
• M-theory, Black Holes and Cosmology
• Quantum gravity phenomenology from the perspective of quantum general relativity and quadratic gravity
• Massive Covariant Colour-Kinematics in 3D
• Dimensional Regularization for the Particle Transition Amplitude in Curved Space
• Superstring amplitudes meet surfaceology
• Extended DBI and its generalizations from graded soft theorems
• On-shell Methods for Form Factors in N=4 SYM and Their Applications
• Co-homology of Differential Forms and Feynman diagrams