论文标题
有关三个时空维度的经典双复制的更多信息
More on the Classical Double Copy in Three Spacetime Dimensions
论文作者
论文摘要
众所周知，三个时空维度（3D）中的一般相对性（GR）没有明确的牛顿限制。最近，在Arxiv：1904.11001中发现了一个模仿预期牛顿电位行为的静态解决方案，通过研究量规理论中的点电荷的经典双拷贝。这是第一个例子，仪表理论中的真空解决方案在重力侧导致非vacuum溶液。由此产生的能量量张量归因于自由标量幽灵场。但是，或者，可以将源视为由空间般的完美流体产生的。在本文中，我们首先给出了解决方案的替代推导，在该解决方案无需执行广义量规转换以获得二次拉格朗日语而无需传播幽灵领域。然后，我们提出了溶液的固定版本，并表明在这种情况下，源的标量场解释无法生存，使空间液的流体是唯一的可能性。我们给出了解决方案的仪表理论单副本，并评论了我们结果对3D经典双复制的有效性的含义。还讨论了宇宙常数的效果。
It is well-known that General Relativity (GR) in three spacetime dimensions (3D) has no well-defined Newtonian limit. Recently, a static solution mimicking the behaviour of the expected Newtonian potential has been found in arXiv:1904.11001 by studying the classical double copy of a point charge in gauge theory. This is the first example where the vacuum solution in the gauge theory leads to a non-vacuum solution on the gravity side. The resulting energy-momentum tensor was attributed to a free scalar ghost field; however, alternatively, the source can be seen as one resulting from a spacelike perfect fluid. In this paper, we first give an alternative derivation of the solution where there is no need to perform a generalized gauge transformation to obtain a quadratic Lagrangian without propagating ghost fields. Then, we present a stationary version of the solution and show that the scalar field interpretation of the source does not survive in this case, leaving the spacelike fluid as the only possibility. We give the gauge theory single copy of our solution and comment on the implications of our results on the validity of the classical double copy in 3D. The effect of the cosmological constant is also discussed.
