Gravitational Radiation from Color-Kinematics Duality

TL;DR

The paper investigates how color-kinematics duality encodes gravitational radiation in a classical scattering setup by comparing YM, BS, and dilaton gravity in the post-Minkowskian regime. It uses worldline formalism to compute radiation to next-to-leading order and constructs duality-satisfying kinematic numerators that satisfy Jacobi identities beyond the S-matrix. The gravitational radiation computed directly in dilaton gravity agrees with the YM double-copy result, generalizing leading-order Goldberger-Ridgway rules. These results indicate that color-kinematics duality and double copy can simplify higher-order calculations in classical gravity and potentially inform gravitational-wave computations.

Abstract

We perturbatively calculate classical radiation in Yang-Mills theory and dilaton gravity, to next-to-leading order in couplings. The radiation is sourced by the scattering of two relativistic massive scalar sources with the dynamical effect taken into account, corresponding to the post-Minkowskian regime in gravity. We show how to arrange the Yang-Mills radiation such that the duality between colors and kinematics is manifest, including the three-term Jacobi identity. The search for duality-satisfying expressions exploits an auxiliary bi-adjoint scalar theory as a guide for locality. The double copy is obtained by replacing the color factors in Yang-Mills with kinematic counterparts, following Bern-Carrasco-Johansson construction in S- matrix. On the gravity side, the radiation is directly computed at the third post-Minkowskian order with massive sources. We find perfect agreement between observables in dilaton gravity and the Yang-Mills double copy. This non-trivially generalizes the leading-order rules by Goldberger and Ridgway. For the first time, the kinematic Jacobi identity appears beyond field-theory S-matrix, suggesting that the color-kinematics duality holds more generally. Our results offer a path for simplifying analytical calculations in post-Minkowskian regime.

Figures (3)

• Figure 1: The diagram on the right is for the radiation in Eq. \ref{['eq:preLO']}, and on the left is the diagram for worldline trajectory and color charge in Eq. \ref{['eq:pos_LO']} and Eq. \ref{['eq:color_LO']} respectively. The solid straight lines are massive sources and the wavy lines are radiations.
• Figure 2: A schematic diagram contributed to next-to-leading order radiation in the same notation as Figure \ref{['fig:LO']}. This becomes a self-energy correction to particle 1 with leading order radiation if we identify the particle 3 with particle 1.
• Figure 3: A schematic diagram which is zero is YM but non-zero in (dilaton) gravity. The conventions follow Figure \ref{['fig:self']} but the wavy lines are gauge fields in YM, or gravitons in gravity. Particle $1$ absorbs the leading-order radiation from $2$ and $3$ before emitting the final radiation. The corresponding color factor is zero by antisymmetry of the structure constant once we identify the color $c_3$ with $c_2$, following the prescription Eq. \ref{['eq:3_body']}. The corresponding diagram is non-zero for gravity.