The Entire Four-Graviton EFT from the Duality Between Color and Kinematics

TL;DR

This paper extends the color-kinematics duality to a universal double-copy framework that encompasses all four-graviton interactions, including higher-derivative operators, revealing a comprehensive structure linking gauge and gravity theories.

Contribution

It generalizes the color-kinematics duality beyond Lie algebras, defining a universal double copy that spans all parity-even four-graviton amplitudes in any dimension.

Findings

Universal double-copy construction for four-graviton amplitudes.

Classification of gauge-theory numerators and gravitational operators.

Explicit expressions provided for gauge and gravity building blocks.

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 $d^{abc}$ 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 $R^3$ 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 ancillary files. 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.