Abstract
Classical double copy is an intriguing relationship between classical solutions to a gravity theory and solutions to classical Yang-Mills equations. Although formally inspired by the double copy relation between (quantum) scattering amplitudes in QCD and perturbative gravity, a direct proof of the former from the latter continues to be under investigation. In this paper, we attempt to prove classical double copy from the color-kinematics duality symmetry of QCD amplitudes in a restricted setting. That is we consider radiative solutions with classical scattering sources in Yang-Mills theory and perturbative gravity in D > 4 spacetime dimensions. We show that when the frequency of radiation is much smaller than the characteristic frequency of the process, then at the subleading order in frequency, the classical double copy relating radiative gluon field to radiative gravitational field can be proved from the color-kinematics duality of QCD amplitudes.
Highlights
Among the many developments in the study of scattering amplitudes in recent years, the discovery of the relationship between scattering amplitudes in gravitational theories with those in gauge theories with color is striking
The other closely related avatar is known as the double copy which is a consequence of an inherent symmetry present in many theories with color
This symmetry is known as color-kinematics duality and is a symmetry which is not manifest in Feynman diagrammatic expansion of amplitudes but becomes manifest when the amplitudes are written in the so-called Bern-Carrasco-Johansson (BCJ) representation [2]
Summary
Among the many developments in the study of scattering amplitudes in recent years, the discovery of the relationship between scattering amplitudes in gravitational theories with those in gauge theories with color is striking. Exchanging the color charges and structure constants of the theory for momenta and three point couplings This procedure of obtaining classical gravitational solutions from solutions to Yang-Mills field equations is known as the classical double copy [3]. Our method of proving the classical double copy crucially relies on the soft expansion and we call it the “soft double copy.” In a nutshell this leads us to an understanding of the classical double copy directly from color-kinematics duality at least for low frequency gluon and graviton radiation.
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