Abstract
We compute the classical effective action of color charges moving along worldlines by integrating out the Yang-Mills gauge field to next-to-leading order in the coupling. An adapted version of the Bern-Carrasco-Johansson (BCJ) double-copy construction known from quantum scattering amplitudes is then applied to the Feynman integrands, yielding the prediction for the classical effective action of point masses in dilaton gravity. We check the validity of the result by independently constructing the effective action in dilaton gravity employing field redefinitions and gauge choices that greatly simplify the perturbative construction. Complete agreement is found at next-to-leading order. Finally, upon performing the post-Newtonian expansion of our result, we find agreement with the corresponding action of scalar-tensor theories known from the literature. Our results represent a proof of concept for the classical double-copy construction of the gravitational effective action and provides another application of a BCJ-like double copy beyond scattering amplitudes.
Highlights
There is a growing body of evidence for a fascinating perturbative duality between Yang-Mills theory and quantum gravity known as the double-copy construction or color-kinematics duality due to Bern, Carrasco and Johansson (BCJ) [1,2,3]
We compute the classical effective action of color charges moving along worldlines by integrating out the Yang-Mills gauge field to next-to-leading order in the coupling
An adapted version of the BernCarrasco-Johansson (BCJ) double-copy construction known from quantum scattering amplitudes is applied to the Feynman integrands, yielding the prediction for the classical effective action of point masses in dilaton gravity
Summary
There is a growing body of evidence for a fascinating perturbative duality between Yang-Mills theory and quantum gravity known as the double-copy construction or color-kinematics duality due to Bern, Carrasco and Johansson (BCJ) [1,2,3]. We generalize these approaches to the double copy of gravitationally interacting binaries by ascending from the level of equations of motion to the classical effective action This approach makes direct contact to the post-Minkowskian (weak-field) and postNewtonian (weak-field and slow-motion) expansions of the gravitational potential for which high-order results exist in the literature, namely at the fourth postNewtonian order (four loop) for nonspinning bodies: using a canonical formalism of general relativity [32], a Fokker Lagrangian [33,34], and partial results within an effective field theory formalism [35]. Our conventions, the Feynman rules and a discussion of self-interactions can be found in the appendices
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