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Entire four-graviton EFT from the duality between color and kinematics

John Joseph M. Carrasco1,2, Sai Sasank Chava1, Alex Edison1,2, Eliseu Kloster3,1,2, and Suna Zekioğlu1

  • 1Amplitudes and Insights Group, Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA
  • 2Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA), Northwestern University, 1800 Sherman Ave, Evanston, Illinois 60201, USA
  • 3Department of Astronomy and Astrophysics, University of Chicago, Chicago, Illinois 60637, USA

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Phys. Rev. D 113, 125008 – Published 5 June, 2026

DOI: https://doi.org/10.1103/fxbh-9sgd

Abstract

The Bern-Carrasco-Johansson (BCJ) double-copy construction reveals a fundamental structural connection between gauge and gravity theories. At its core, the BCJ double copy is directly due to a duality between the algebraic relations of a color root and those of a kinematic root. We generalize this principle beyond the conventional Lie algebra structure of tree-level Yang-Mills theory. By demanding color-kinematics duality for the complete basis of four-point color structures—including those involving the symmetric dabc constants—we define the universal double copy. We systematically classify the bases of all such parity-even generalized gauge-theory numerators and, independently, the space of all parity-even four-graviton higher-derivative operators. We demonstrate that our universal double-copy construction precisely spans the entire tower of parity-even four-graviton amplitudes in any dimension, except for the Lovelock R3 contribution in D>6 which we can express in terms of a particularly simple universal triple-copy involving gauge theories coupled to scalars. Explicit machine-readable expressions for the complete basis of gauge-theory numerators and fundamental gravitational building blocks are provided in the Supplemental Material. This establishes that all possible four-point gravitational interactions can be factorized into products of gauge-theory building blocks governed by this universal notion of color-kinematics duality.

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Phys. Rev. D 113, 125008– Published 5 June, 2026
  • Received 18 January 2026
  • Accepted 21 April 2026
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