Equivalent D=3 Supergravity Amplitudes from Double Copies of Three-Algebra and Two-Algebra Gauge Theories

Abstract

We show that three-dimensional supergravity amplitudes can be obtained as double copies of either three-algebra super-Chern-Simons matter theory or that of two-algebra super-Yang-Mills theory, when either theory is organized to display the color-kinematics duality. We prove that only helicity-conserving four-dimensional gravity amplitudes have nonvanishing descendants when reduced to three dimensions; implying the vanishing of odd-multiplicity S-matrix elements, in agreement with Chern-Simons matter theory. We explicitly verify the double-copy correspondence at four and six points for N=12,10,8 supergravity theories and discuss its validity for all multiplicity.

5 pages, published version in PRL

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• Gravity Amplitudes as Generalized Double Copies
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• The pure BRST Einstein-Hilbert Lagrangian from the double-copy to cubic order
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• Biadjoint wires
• Unraveling conformal gravity amplitudes
• Overcoming Obstacles to Colour-Kinematics Duality at Two Loops
• $D=6$, $\mathcal{N}=(2,0)$ and $\mathcal{N}=(4,0)$ theories
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• Generalizations of the Double-Copy: the KLT Bootstrap
• Scattering Amplitudes and the Double Copy in Topologically Massive Theories
• On powercounting in perturbative quantum gravity theories through color-kinematic duality
• On Three-Algebra and Bi-Fundamental Matter Amplitudes and Integrability of Supergravity
• Global symmetries of Yang-Mills squared in various dimensions
• Gauge $\times$ Gauge on Spheres
• The momentum amplituhedron of SYM and ABJM from twistor-string maps
• Non-planarity through unitarity in ABJM
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• Double Copy from Tensor Products of Metric BV${}^{■}$-algebras
• Scattering Amplitudes of Kaluza-Klein Strings and Extended Massive Double-Copy
• Explicit BCJ numerators of nonlinear sigma model
• Tree-Level Color-Kinematics Duality from Pure Spinor Actions
• ABJM amplitudes and WL at finite N
• Color-Kinematic Duality in ABJM Theory Without Amplitude Relations
• Spontaneously Broken Yang-Mills-Einstein Supergravities as Double Copies
• Massive Color-Kinematics Duality and Double-Copy for Kaluza-Klein Scattering Amplitudes
• Next-to-MHV Yang-Mills kinematic algebra
• Scattering Amplitudes of Massive N=2 Gauge Theories in Three Dimensions
• The Weyl double copy from twistor space
• Projectivity of Planar Zeros in Field and String Theory Amplitudes
• Topological Equivalence Theorem and Double-Copy for Chern-Simons Scattering Amplitudes
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• Entire Four-Graviton EFT from the Duality Between Color and Kinematics
• Ersatz gravity and black-hole thermodynamics from Manin gauge theory with noncompact gauge group