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The Duality Between Color and Kinematics and its Applications
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The Duality Between Color and Kinematics and its Applications
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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.
Forward citations
Cited by 35 Pith papers
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On the Inverse Problem in Effective Field Theory
The tree-level spectrum of heavy particles can be extracted from EFT Wilson coefficients using new nonlinear analytic dispersion relations, exactly for finite resonances and approximately otherwise.
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Twisted de Rham theory for string double copy in AdS
Noncommutative twisted de Rham theory derives the intersection number of open-string contours whose inverse is the double-copy kernel for four-point AdS string generating functions.
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Light-Front approach to $4d$ massless Higher-Spin interactions
Solving Poincaré-algebra closure at quartic order yields infinitely many local 4d massless higher-spin theories (finite or infinite spectra), classifies chiral one-/two-derivative models, and determines all local unit...
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Light-Front approach to $4d$ massless Higher-Spin interactions
Quartic Poincaré-closure in the light-front gauge classifies all one- and two-derivative chiral higher-spin theories in 4d and yields new finite-spectrum local theories and quasi-chiral families.
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Kerr Soft Dressing and the $w_{1+\infty}$ Frame Algebra at Null Infinity
The Kerr soft exponent generates a parity-alternating hierarchy of null-infinity frame generators—displacement memory at s=0, spin memory at s=1, and higher moments alternating by Kerr multipole parity—realized as the...
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Magic without a phase: phase-independent stabilizer R\'enyi entropy in gluon scattering
A phase-averaged stabilizer Rényi entropy is introduced for tree-level gluon scattering, with color-independent phase-independent magic that is larger in 3→2 than 2→2 and has a soft-limit lower bound in 2→3.
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Dyeing form factors as amplitudes
A dyeing procedure maps form factors to colored amplitudes, recovering the originals by bleaching and explaining double-copy features through standard BCJ relations.
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Massless spinning fields on the Light-Front: quartic vertices and amplitudes
A light-front quartic-constraint analysis classifies local massless higher-spin vertices and amplitudes, yielding no-go results for unitary theories and new quasi-chiral higher-spin sectors.
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Entire Four-Graviton EFT from the Duality Between Color and Kinematics
Every parity-even four-graviton amplitude in any spacetime dimension can be constructed from gauge-theory building blocks via double or triple color-kinematics copies, with the D>6 Lovelock R^3 term as the unique trip...
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Structure of Chern-Simons Graviton Scattering Amplitudes from Topological Graviton Equivalence Theorem and Double Copy
Establishes the Topological Graviton Equivalence Theorem to prove large energy cancellations in N-point massive graviton amplitudes and constructs three- and four-point amplitudes via double copy from topologically ma...
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$D$-Dimensional Modular Assembly of Higher-Derivative Four-Point Contact Amplitudes Involving Fermions
A modular assembly method constructs D-dimensional higher-derivative four-point amplitudes involving fermions from gauge-invariant blocks, color factors, and permutation-invariant scalar polynomials.
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Generalized Unitarity Method for Worldline Field Theory
Worldline gravitational observables can be bootstrapped from locality, unitarity, gauge invariance, and a soft theorem once worldline energies are complexified, reproducing the known O(G^5/2) waveform and O(G^3) on-sh...
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An adaptive inverse-problem framework for one-loop five-gluon BCJ numerators
The complete 207-dimensional family of one-loop five-gluon BCJ numerator coefficients is reconstructed exactly, and every direction in that family is shown to be invisible to the specified color-ring observable.
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Color-factor symmetry using perturbiner methods for tree-level amplitudes of Yang-Mills theory coupled to matter
A new perturbiner proof shows tree-level Yang-Mills amplitudes with any number of fundamental scalars or spinors and at least one gluon are invariant under color-factor shifts, yielding BCJ relations.
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Color-factor symmetry using perturbiner methods for tree-level amplitudes of Yang-Mills theory coupled to matter
Perturbiner recursion proves color-factor symmetry (hence BCJ relations) for all tree-level YM+matter amplitudes with at least one gluon.
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Uniqueness and Analytic Structures of Bosonic String Effective Amplitudes
Gauge invariance, locality, and cyclicity uniquely fix dimension-raising operators for zero-transcendentality bosonic string amplitudes, yielding recursive construction from Yang-Mills and factorization via inverse op...
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Planar loop integrands from cuts in $D$ dimensions
A Möbius-inversion formula on the refinement poset reconstructs planar L-loop n-point integrands as sums over non-scaleless scalar graphs dressed by D-dimensional cuts, demonstrated for Yang-Mills theory.
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Non-topological solitons in biadjoint scalar field theory
Biadjoint scalar theory admits a family of non-topological solitons carrying U(1) charge, time-dependent like Q-balls, stable in truncation, with finite localized energy.
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Double copy of form factors with multiple operator insertions
A dyeing procedure generalizes the double copy to form factors with multiple operator insertions by mapping spurious poles to physical propagators and revealing a new scalar-ordering structure in gravity.
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Quantum graviton scattering with definite helicities in the null surface formulation. III: Fourth-order recursion and ultraviolet finiteness
A fourth-order null-surface computation is presented as completing the tree-level 2-to-2 graviton amplitude and establishing all-loop UV finiteness, but the verification is left conditional and one partial-fraction id...
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Quantum graviton scattering with definite helicities in the null surface formulation. III: Fourth-order recursion and ultraviolet finiteness
Computation of σ⁺₄ in the null surface formulation establishes UV-finiteness of the graviton S-matrix at all loops and reproduces the tree-level Weinberg-DeWitt amplitude from specific perturbative orders.
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Tree Amplitudes with Charged Matter in Pure Gauge Theory
A new Mathematica package computes tree amplitudes with arbitrary gauge bosons and arbitrarily charged massless fermions by reducing distinct-flavor partial amplitudes to linear combinations of single-flavor supersymm...
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Residual Symmetries and Their Algebras in the Kerr-Schild Double Copy
The Kerr-Schild double copy enlarges residual symmetries at the ansatz level but preserves physical symmetries after cohomological reduction, exposing a mismatch between Yang-Mills and gravity residual symmetry structures.
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Graviton Photoproduction by a Kerr-Newman Black Hole with Worldline EFT
The graviton-to-photon conversion amplitude for a Kerr-Newman black hole is computed through O(S^2) in the long-wavelength worldline EFT and shown to be fully determined by the black hole's electromagnetic and mass mu...
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The Penrose Transform and the Kerr-Schild double copy
The Kerr-Schild and twistorial double copies are equivalent for self-dual vacuum Kerr-Schild spacetimes.
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Hawking Radiation meets the Double Copy
Bogoliubov coefficients from scattering a scalar in a collapsing EM background (single copy of Vaidya) match ray-tracing results and connect to Hawking radiation through the double copy.
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Hidden zeros for higher-derivative YM and GR amplitudes at tree-level
Hidden zeros extend to higher-derivative tree-level gluon and graviton amplitudes, with systematic cancellation of propagator singularities shown via bi-adjoint scalar expansions.
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Relativistic Particle on Light-Front
A front-form construction with a reference null vector makes the massive-to-massless Wigner classification continuous and derives the massless spin-1 polarization shift coefficient from the angle between reference vectors.
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NLO Angular Impulse and Leading Singularities to all orders in spin for Kerr Black Holes
NLO angular impulse for Kerr black holes computed to all orders in spin via KMOC formalism and leading singularities, with consistency checks and potential extraction.
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Residual Symmetries and Their Algebras in the Kerr-Schild Double Copy
The Kerr-Schild double copy does not map residual symmetries between Yang-Mills and gravity; gravitational conformal Killing vectors are shown to be BRST-exact after a Weyl-compensated complex, leaving only global isometries.
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Color Decompositions of the Two Loop Amplitudes of Yang-Mills theory
The paper decomposes two-loop Yang-Mills gluon amplitudes into color structures via trace and structure-constant bases and organizes relations between the resulting partial amplitudes.
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Hidden Zeros and $2$-split via BCFW Recursion Relation
Hidden zeros in NLSM amplitudes are proven via modified BCFW recursion, with 2-split holding only under careful current definition.
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Note on hidden zeros and expansions of tree-level amplitudes
Hidden zeros in tree-level amplitudes of several theories are attributed to zeros of bi-adjoint scalar amplitudes via universal expansions, with a mechanism shown to cancel potential propagator divergences in gravity.
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Lecture notes: Introduction to the Off-shell Double Copy Program
Self-contained lecture notes introduce the off-shell single/double copy relating Yang-Mills and DFDF gauge theories to Einstein-Hilbert, Weyl gravity and NS-NS supergravity via Kerr-Schild and Double Field Theory.
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Lecture notes: Introduction to the Off-shell Double Copy Program
Lecture notes reviewing gauge and gravitational theories to present the off-shell single and double copy, including T-duality approaches.
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