Pure Gravities via Color-Kinematics Duality for Fundamental Matter

Abstract

We give a prescription for the computation of loop-level scattering amplitudes in pure Einstein gravity, and four-dimensional pure supergravities, using the color-kinematics duality. Amplitudes are constructed using double copies of pure (super-)Yang-Mills parts and additional contributions from double copies of fundamental matter, which are treated as ghosts. The opposite-statistics states cancel the unwanted dilaton and axion in the bosonic theory, as well as the extra matter supermultiplets in supergravities. As a spinoff, we obtain a prescription for obtaining amplitudes in supergravities with arbitrary non-self-interacting matter. As a prerequisite, we extend the color-kinematics duality from the adjoint to the fundamental representation of the gauge group. We explain the numerator relations that the fundamental kinematic Lie algebra should satisfy. We give nontrivial evidence supporting our construction using explicit tree and loop amplitudes, as well as more general arguments.

48 pages + refs, 15 figures, 3 tables; v2 minor corrections, journal version

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• A new gauge-invariant double copy for heavy-mass effective theory
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• Topology and Wilson lines: global aspects of the double copy
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• On the kinematic algebra for BCJ numerators beyond the MHV sector
• Kinematic Jacobi Identity is a Residue Theorem: Geometry of Color-Kinematics Duality for Gauge and Gravity Amplitudes
• Double-Copy Constructions and Unitarity Cuts
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• Complete construction of magical, symmetric and homogeneous N=2 supergravities as double copies of gauge theories
• Twin Supergravities from Yang-Mills Squared
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• Expansion of All Multitrace Tree Level EYM Amplitudes
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• The double copy for heavy particles
• BCJ duality and double copy in the closed string sector
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• Manifesting enhanced cancellations in supergravity: integrands versus integrals
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• Positive helicity Einstein-Yang-Mills amplitudes from the Double Copy
• String-motivated one-loop amplitudes in gauge theories with half-maximal supersymmetry
• Kinematic Hopf algebra for amplitudes and form factors
• Perfecting one-loop BCJ numerators in SYM and supergravity
• BCJ Identities and $d$-Dimensional Generalized Unitarity
• KLT-type relations for QCD and bicolor amplitudes from color-factor symmetry
• Proof of a new colour decomposition for QCD amplitudes
• Double copies of fermions as only gravitational interacting matter
• One-loop Amplitudes for N=2 Homogeneous Supergravities
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• Double Copy from Tensor Products of Metric BV${}^{■}$-algebras
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• The Full-Color Two-Loop Four-Gluon Amplitude in $\mathcal{N}=2$ Super-QCD
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• The Mile High Magic Pyramid
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