非交换张量纳维-斯托克斯方程的同伦双拷贝和Kawai-Lewellen-Tye关系
Homotopy double copy and the Kawai-Lewellen-Tye relations for the non-abelian and tensor Navier-Stokes equations
摘要：
最近，非阿贝尔推广的纳维-斯托克斯方程，表现出明显的颜色和运动学之间的二元性已被张和Mangan提出。在本文中，我们提供了一个新的角度对这个方程的双副本制定，根据Borsten，Kim，Jurčo，Macrelli，Saemann和Wolf提出的同伦代数图片。在这个过程中，我们精确地描述了如何双拷贝可以实现在微扰扩展的水平。具体来说，我们将表明，颜色打扮的贝伦兹-吉勒电流的非阿贝尔版本的纳维-斯托克斯方程可以用来构建的贝伦兹-吉勒电流的双重复制方程，通过替换的颜色因子与第二个副本的运动分子。我们还将展示一个Kawai-Lewellen-Tye关系，说明后者中的全部树级散射振幅可以被写为前者中树级色序部分振幅的乘积。
英文摘要：
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, Jurčo, 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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