Radiation and the classical double copy for color charges

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.

• The paper demonstrates that classical Yang-Mills solutions with color charges can be directly mapped to dilaton gravity fields using double copy rules.
• Utilizing color-to-kinematics replacements, the authors derive perturbative solutions that simplify gravitational waveform modeling in astrophysical events.
• The study extends BCJ amplitude relations to classical fields, providing a parameter-free framework linking gauge theories with gravity.

Essay on "Radiation and the Classical Double Copy for Color Charges"

The paper "Radiation and the Classical Double Copy for Color Charges" by Goldberger and Ridgway presents a significant exploration into the classical double copy correspondence, wherein classical solutions of Yang-Mills (YM) theory with color charges are directly mapped into solutions in a gravitational theory that includes a graviton and a dilaton field. This investigation builds directly upon the Bern-Carrasco-Johansson (BCJ) relationships, which originally revealed a profound connection between gauge theories and gravity in terms of scattering amplitudes. This paper extends similar ideas into the field of classical fields, yielding potentially valuable insights and implications for gravitational waveform calculations relevant to astrophysical phenomena.

Overview of Main Results

The paper reports on the construction of perturbative classical solutions to the Yang-Mills equations when coupled with point particles carrying color charge. Through the application of a set of color-to-kinematics replacement rules, originally introduced by Bern, Carrasco, and Johansson, the authors generate analogous solutions in a $d$-dimensional dilaton gravity model. The perturbative solutions in YM theory are shown to have a direct correspondence with those in dilaton gravity, which contains a graviton and a scalar (dilaton) field. Notably, this correspondence implies a conceptual mapping between non-Abelian particles and gravitating sources that carry dilaton charge.

In the limit where these color charges become highly relativistic, dilaton exchange decouples from the gravitational interactions, resulting in solutions that effectively reflect those of pure gravity. This suggests a potential simplification pathway for calculating gravitational waveforms in scenarios such as black hole mergers, by leveraging more computationally tractable YM gluon radiation calculations. This aspect is notable for its practicality in astrophysical applications, particularly in generating templates for gravitational-wave observatories like LIGO.

Theoretical Implications

The results presented in the paper enhance the understanding of the structural parallels between YM theory and general relativity by establishing a classical double copy relation between YM fields due to color charges and gravitational fields in a theory including a dilaton. While the BCJ relations had established such connections at the level of scattering amplitudes, this work extends the applicability to classical fields, a field where the dynamics involve an infinite series of perturbative contributions rather than finite tree-level diagrams as in quantum amplitudes.

The classical double copy presented is parameter-free, independent of spacetime dimensions upon considering the specific setups outlined. This independence is a valuable feature because it suggests that the double copy relations could hold broadly across different scenarios within both quantum and classical contexts.

Speculation on Future Developments

Given the results obtained, several avenues for future research and development appear promising. Notably, the computational techniques that bypass the need for direct gravitational dynamics by using YM solutions may find broader application in complex gravitational systems. Further extensions could involve examining how spinning particles are mapped within this framework, potentially introducing additional fields like the two-form gauge field $B_{\mu\nu}$.

Additionally, the realization that the perturbative double copy reduces to pure general relativity in the context of massless point particles offers a more direct computational path for relating YM fields and gravitational wave sources in high-energy astrophysical events. Addressing specific limits, such as large spacetime dimensions or high-energy particles, could yield insights into the behavior of complex gravitational systems and may offer new methods for simulating or analyzing such systems with a high degree of accuracy and reduced computational cost.

Conclusion

In summary, the work by Goldberger and Ridgway deepens the understanding of the classical double copy principle, forging new paths for both theoretical exploration and practical computational techniques in the study of gravitational dynamics. While firmly grounded in the rich theoretical framework of BCJ, this paper invites further research, potentially impacting areas as diverse as gravitational wave astronomy and theoretical particle physics.