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Radiation and the classical double copy for color charges

Walter D. Goldberger, Alexander K. Ridgway

TL;DR

The paper develops a perturbative classical correspondence between Yang-Mills theory with dynamical color charges and a gravity-dilaton system, via BCJ-inspired color-to-kinematics substitutions. By computing the radiative observables of classical color charges and applying the double-copy rules, it shows that the YM radiation maps to combined graviton and dilaton radiation, with the dilaton typically persisting except in massless or large-d limits where pure GR is recovered. The results demonstrate that Kerr–Schild duality does not hold universally at finite mass and dimension, though it re-emerges in special limits, and they propose potential applications to generating gravitational-wave templates from gauge-theory calculations. The work clarifies the role of the dilaton and related fields in the classical double copy and suggests avenues for extending the framework to spinning sources and higher-order perturbative corrections.

Abstract

We construct perturbative classical solutions of the Yang-Mills equations coupled to dynamical point particles carrying color charge. By applying a set of color to kinematics replacement rules first introduced by Bern, Carrasco and Johansson (BCJ), these are shown to generate solutions of d-dimensional dilaton gravity, which we also explicitly construct. Agreement between the gravity result and the gauge theory double copy implies a correspondence between non-Abelian particles and gravitating sources with dilaton charge. When the color sources are highly relativistic, dilaton exchange decouples, and the solutions we obtain match those of pure gravity. We comment on possible implications of our findings to the calculation of gravitational waveforms in astrophysical black hole collisions, directly from computationally simpler gluon radiation in Yang-Mills theory.

Radiation and the classical double copy for color charges

TL;DR

The paper develops a perturbative classical correspondence between Yang-Mills theory with dynamical color charges and a gravity-dilaton system, via BCJ-inspired color-to-kinematics substitutions. By computing the radiative observables of classical color charges and applying the double-copy rules, it shows that the YM radiation maps to combined graviton and dilaton radiation, with the dilaton typically persisting except in massless or large-d limits where pure GR is recovered. The results demonstrate that Kerr–Schild duality does not hold universally at finite mass and dimension, though it re-emerges in special limits, and they propose potential applications to generating gravitational-wave templates from gauge-theory calculations. The work clarifies the role of the dilaton and related fields in the classical double copy and suggests avenues for extending the framework to spinning sources and higher-order perturbative corrections.

Abstract

We construct perturbative classical solutions of the Yang-Mills equations coupled to dynamical point particles carrying color charge. By applying a set of color to kinematics replacement rules first introduced by Bern, Carrasco and Johansson (BCJ), these are shown to generate solutions of d-dimensional dilaton gravity, which we also explicitly construct. Agreement between the gravity result and the gauge theory double copy implies a correspondence between non-Abelian particles and gravitating sources with dilaton charge. When the color sources are highly relativistic, dilaton exchange decouples, and the solutions we obtain match those of pure gravity. We comment on possible implications of our findings to the calculation of gravitational waveforms in astrophysical black hole collisions, directly from computationally simpler gluon radiation in Yang-Mills theory.

Paper Structure

This paper contains 11 sections, 82 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Classical Yang-Mills solutions
  3. Equations of motion and classical observables
  4. Perturbative solutions
  5. Classical solutions in dilaton gravity
  6. The leading order radiation fields
  7. Color-kinematics correspondence
  8. The double copy of a static point source
  9. Pure gravity and the double copy for massless particles
  10. Discussion and Outlook
  11. Acknowledgments

Figures (3)

  • Figure 1: Leading order Feynman diagrams for the perturbative expansion of ${\tilde{J}}^\mu_a(k)$.
  • Figure 2: Leading order Feynman diagrams in the perturbative expansion of ${\tilde{T}}^{\mu\nu}(k)$.
  • Figure 3: Leading order Feynman diagrams in the perturbative expansion of the scalar emission amplitude ${\cal A}_s(k)$.