Classical gluon and graviton radiation from the bi-adjoint scalar double copy

TL;DR

Using a bi-adjoint scalar theory with cubic interactions as a zeroth copy, the paper demonstrates a two-step double copy that connects perturbative classical radiating solutions in Yang–Mills to gravity. By applying color–kinematics substitutions $c^a\to p^7$, $[\tilde{c},\tilde{c}]^a\to\Gamma^{\mu\nu\rho}$, the authors construct radiation amplitudes ${\cal A}^{a\tilde{a}}(k)$ and obtain the gravitational image ${\hat{\cal A}}^{\mu\nu}(k)$ with $k^2=0$, matching dilaton–gravity radiation patterns. At leading order, the double-copy currents coincide with gauge-theory structures up to improvement terms, and at ${\cal O}(g^2)$ the Yang–Mills three-gluon content emerges from the bi-adjoint calculation, illustrating a consistent two-fold double copy. The approach promises a simplification for computing gravitational radiation from compact objects but requires higher-order checks and a reliable projection of dilaton/B-field modes to realize pure gravity observables.

Abstract

We find double copy relations between classical radiating solutions in Yang-Mills theory coupled to dynamical color charges and their counterparts in a cubic bi-adjoint scalar field theory which interacts linearly with particles carrying bi-adjoint charge. The particular color-to-kinematics replacements we employ are motivated by the BCJ double copy correspondence for on-shell amplitudes in gauge and gravity theories. They are identical to those recently used to establish relations between classical radiating solutions in gauge theory and in dilaton gravity. Our explicit bi-adjoint solutions are constructed to second order in a perturbative expansion, and map under the double copy onto gauge theory solutions which involve at most cubic gluon self-interactions. If the correspondence is found to persist to higher orders in perturbation theory, our results suggest the possibility of calculating gravitational radiation from colliding compact objects, directly from a scalar field with vastly simpler (purely cubic) Feynman vertices.

Figures (1)

• Figure 1: Leading order Feynman diagrams for the perturbative expansion of ${\tilde{J}}^\mu_a(k)$.