Homotopy double copy and the Kawai–Lewellen–Tye relations for the non-abelian and tensor Navier–Stokes equations
Valentina Guarín Escudero, Cristhiam Lopez-Arcos, Alexander Quintero Vélez
Abstract
Recently, a non-abelian generalization of the Navier–Stokes equation that exhibits a manifest duality between color 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, Jurčo, Macrelli, Saemann, and Wolf. In the process, we describe precisely how the double copy can be realized at the level of perturbiner expansions. Specifically, we will show that the color-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 color 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 color ordered partial amplitudes in the former.