论文标题
在Lagrangian配方双副本到立方顺序
On the Lagrangian formulation of the double copy to cubic order
论文作者
论文摘要
我们研究了仪表理论与重力之间的双拷贝对应关系的拉格朗日公式，直到立方顺序。以双拷贝场的定义为两个向量的卷积为基础，我们获得了自由的重力lagrangians作为两个Yang-Mills Lagrangians的产品，其形式可轻松扩展到大规模的情况。我们讨论了这些结果来自无张力的字符串的起源，并显示了量规固定的存在，它们混合了两个旋转一个部门，并导致了自由拉格朗日的替代版本，尤其是简单的版本。然后，我们通过Noether程序构造了完整双拷贝多重组的立方顶点，其中包括重力，两种形式和标量粒子。在自由和立方水平下，结果仅在仪表不变性之上强加了左右Lorentz对称性统治收缩，这是在双层副本领域之间的左右对称性统治收缩。尽管结果很好地匹配了$ \ Mathcal {n} = 0 $超级强烈的立方相互作用，包括标量粒子和两种形式之间的量规不变耦合，但这么两折的洛伦兹对称性似乎与触视的时空几何相互作用冲突。
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.
