Radiative double copy for Einstein-Yang-Mills theory

Recently, a double-copy formalism was used to calculate gravitational radiation from classical Yang-Mills radiation solutions. This work shows that the Yang-Mills theory coupled to a biadjoint scalar field admits a radiative double copy that agrees with solutions in the Einstein-Yang-Mills theory at the lowest finite order. Within this context, the trace-reversed metric ${\overline{h}}^{\mu \nu }$ 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.

Figure 1

These diagrams represent all of the contributions to ${\widehat{J}}^{\mu a}$ in Yang-Mills-biadjoint-scalar theory. Straight lines represent matter fields, curly lines represent Yang-Mills fields, and double-dashed lines represent biadjoint scalar fields. Diagrams 1(a), 1(b), 1(d), and 1(e) correspond to $J^{\mu a}(k)$, while diagrams 1(c) and 1(f) correspond to $j^{\mu a}(k)$.

Figure 2

These diagrams represent all of the contributions to ${\widehat{T}}^{\mu \nu }$ in the Einstein-Yang-Mills theory. The wavy lines represent gravitational fields, the dashed lines represent dilaton fields, and the curly lines represent Yang-Mills fields. Diagrams 2(a), 2(b), 2(d), 2(e), 2(g), and 2(h) correspond to $\sqrt{|g|}{T}^{\mu \nu }(k)$, while diagrams 2(c), 2(f), and 2(i) correspond to ${\widehat{t}}^{\mu \nu }(k)$.