Homotopy double copy for the non-abelian and tensor Navier–Stokes equations

What is it about?

Recently, a non-abelian generalisation of the Navier-Stokes equation that exhibits a manifest duality between colour and kinematics has been proposed by Cheung and Mangan. In this paper, we offer a new perspective on the double copy formulation of this equation, based on the homotopy algebraic picture suggested by Borsten, Kim, Jurco, Macrelli, Saemann, and Wolf. In the process, we describe precisely how the double copy can be realised at the level of perturbiner expansions. Specifically, we will show that the colour-dressed Berends-Giele currents for the non-abelian version of the Navier-Stokes equation can be used to construct the Berends-Giele currents for the double copied equation by replacing the colour factors with a second copy of kinematic numerators. We will also show a Kawai-Lewellen-Tye relation stating that the full tree-level scattering amplitudes in the latter can be written as a product of tree-level colour ordered partial amplitudes in the former.

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Why is it important?

One motivation for this investigation is that the non-abelian Navier-Stokes equation is rich enough to elucidate the general structure of the double copy prescription, avoiding many of the technical complications that arise in the generic situation. Also, the approach that we have followed has the virtue of giving us the proper arena for understanding the algebraic origins and different incarnations of the double copy procedure.

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