论文标题
来自各个维度的散射幅度的Schwarzschild-Tangherlini度量
The Schwarzschild-Tangherlini metric from scattering amplitudes in various dimensions
论文作者
论文摘要
我们通过从大量标量场发出的重力的多环顶点函数中提取经典贡献来得出静态Schwarzschild-Tangherlini度量。在每个循环订单下，经典的贡献与无数日落积分给出的独特主体不可或缺。通过计算一般维度的散射幅度最高为三环订单，我们明确地将度量的扩展推导到四个，五和六个维度中的第四次后 - 康科夫斯基订单$ O（G_N^4）$。通过引入更高衍生的非最小耦合，有一些紫外线差异被取消。标准的Schwarzschild-Tangherlini是通过通过从de Donder仪条件引起的适当坐标转换来吸收其效应来恢复的。
We derive the static Schwarzschild-Tangherlini metric by extracting the classical contributions from the multi-loop vertex functions of a graviton emitted from a massive scalar field. At each loop orders the classical contribution is proportional to a unique master integral given by the massless sunset integral. By computing the scattering amplitudes up to three-loop order in general dimension, we explicitly derive the expansion of the metric up to the fourth post-Minkowskian order $O(G_N^4)$ in four, five and six dimensions. There are ultraviolet divergences that are cancelled with the introduction of higher-derivative non-minimal couplings. The standard Schwarzschild-Tangherlini is recovered by absorbing their effects by an appropriate coordinate transformation induced from the de Donder gauge condition.
