标题： 关于三次项的双拷贝的拉格朗日表述 显示英文标题

标题： On the Lagrangian formulation of the double copy to cubic order

摘要： 我们研究了规范理论与引力之间双拷贝对应关系的拉格朗日表述，直到三次项为止。基于双拷贝场定义为两个矢量卷积的方法，我们得到了自由引力拉格朗日量，它们是两个杨-米尔斯拉格朗日量的乘积，并且易于扩展到有质量的情况。我们讨论了这些结果来自张力弦的起源，并展示了存在混合两个自旋-1 部分的规范固定方法，从而导致自由拉格朗日量的一个特别简单的替代版本。然后，我们通过诺特定理构造了完整的双拷贝多重重子的所有三次顶点，其中包括一个引力子、一个二形式和一个标量粒子。无论是自由情况还是三次情况下，结果都唯一地由规范不变性和左右洛伦兹对称性来决定，该对称性控制着双拷贝场之间的指标收缩。尽管结果很好地匹配了 $\mathcal{N}=0$ 超引力的三次相互作用，包括标量粒子和二形式之间的规范不变耦合，但这种双重洛伦兹对称性似乎与时空几何的摄动重建相冲突。 显示英文摘要

摘要： We investigate the Lagrangian formulation of the double-copy correspondence between gauge theories and gravity, up to the cubic order. Building on the definition of the double-copy field as a convolution of two vectors, we obtain free gravitational Lagrangians as products of two Yang-Mills Lagrangians, in a form amenable to be easily extended to the massive case. We discuss the origin of these results from tensionless strings and show the existence of gauge fixings that mix the two spin-one sectors and lead to an alternative, especially simple, version of the free Lagrangian. We then construct cubic vertices for the full double-copy multiplet, comprising a graviton, a two-form and a scalar particle, by means of the Noether procedure. Both at the free and at the cubic level the result gets uniquely fixed only upon imposing, on top of gauge invariance, a left-right Lorentz symmetry ruling contraction of indices among double-copy fields. Whereas the outcome nicely matches the cubic interactions of $\mathcal{N}=0$ supergravity, including the gauge-invariant coupling between the scalar particle and the two-form, such a twofold Lorentz symmetry seems to conflict with the perturbative reconstruction of space-time geometry.