Explicit Formulae for Yang-Mills-Einstein Amplitudes from the Double Copy

Abstract

Using the double-copy construction of Yang-Mills-Einstein theories formulated in our earlier work, we obtain compact presentations for single-trace Yang-Mills-Einstein tree amplitudes with up to five external gravitons and an arbitrary number of gluons. These are written as linear combinations of color-ordered Yang-Mills trees, where the coefficients are given by color/kinematics-satisfying numerators in a Yang-Mills+ϕ^3 theory. The construction outlined in this paper holds in general dimension and extends straightforwardly to supergravity theories. For one, two, and three external gravitons, our expressions give identical or simpler presentations of amplitudes already constructed through string-theory considerations or the scattering equations formalism. Our results are based on color/kinematics duality and gauge invariance, and strongly hint at a recursive structure underlying the single-trace amplitudes with an arbitrary number of gravitons. For the single-graviton case, we give amplitudes to any loop order and obtain, through gauge invariance, new loop-level amplitude relations for Yang-Mills theory.

36 pages, 3 figures, v2: minor corrections, journal version

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• The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy
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• Properties of scattering forms and their relation to associahedra
• Kinematic Hopf algebra for amplitudes and form factors
• Positive helicity Einstein-Yang-Mills amplitudes from the Double Copy
• Perfecting one-loop BCJ numerators in SYM and supergravity
• Quantizing the non-linear graviton
• Scattering of Gravitons and Spinning Massive States from Compact Numerators
• Expansion of Einstein-Yang-Mills theory by Differential Operators
• One-loop Amplitudes for N=2 Homogeneous Supergravities
• Multiparticle solutions to Einstein's equations
• Color-kinematics duality, double copy and the unitarity method for higher-derivative QCD and quadratic gravity
• Double copy for Lagrangians at trilinear order
• Off-shell extended graphic rule and the expansion of Berends-Giele currents in Yang-Mills theory
• Unified web for expansions of amplitudes
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• Worldline description of a bi-adjoint scalar and the zeroth copy
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• Chiral Splitting and $\mathcal{N}=4$ Einstein--Yang--Mills Tree Amplitudes in 4d
• Supersymmetry constraints on U-duality invariant deformations of $N\ge 5$ Supergravity
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• Evaluating EYM amplitudes in four dimensions by refined graphic expansion
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• Algebraic Consistency and Explicit Construction of One-Loop BCJ Numerators of Yang-Mills and Related Theories
• Entire Four-Graviton EFT from the Duality Between Color and Kinematics
• Leading singularities in higher-derivative Yang-Mills theory and quadratic gravity