Abstract
Recently, a double-copy formalism was used to calculate gravitational radiation from classical Yang-Mills radiation solutions. This work shows that Yang-Mills theory coupled to a biadjoint scalar field admits a radiative double copy that agrees with solutions in Einstein-Yang-Mills theory at the lowest finite order. Within this context, the trace-reversed metric $\bar{h}^{\mu\nu}$ is a natural double copy of the gauge boson $A^{\mu a}$. This work provides additional evidence that solutions in gauge and gravity theories are related, even though their respective Lagrangians and nonlinear equations of motion appear to be different.
Highlights
The Lagrangians and equations of motion for gauge and gravity theories appear to be rather different
The BCJ double-copy relations are based on color-kinematics duality, which gives simple constructions of gravity amplitudes starting from gaugetheory amplitudes
While this paper focuses on classical solutions that could be calculated with more traditional methods [45,46,47,48,49,50,51,52,53,54], the hope is that the radiative double copy could help with difficult calculations that may be more cumbersome to do in general relativity alone
Summary
The Lagrangians and equations of motion for gauge and gravity theories appear to be rather different. There are intriguing double-copy connections between their solutions This includes the Kawai-Lewellen-Tye (KLT) tree-level relations between gauge and gravity amplitudes in string theory [1] and the Bern-Carrasco-Johansson (BCJ) double-copy relations between diagrams in quantum field theory [2]. This work builds off the radiative double copy for general relativity found by Goldberger and Ridgway [41] to find gravitational radiation in Einstein-Yang-Mills theory. Motivation for a perturbative double copy can be seen at the Lagrangian level, as the linearized gravity Lagrangian is quite similar to the QED Lagrangian, a linearized version of the Yang-Mills Lagrangian These two theories both have an analogous linearized wave equation. Radiation solutions of nonlinear gauge and gravity theories are related, at least when iterated perturbatively. Appendix A calculates details of the gravitational contribution to the energy momentum pseudotensor and Appendix B gives radiative Feynman rules for simple diagrams with three-point vertices
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