论文标题
两个蝴蝶的故事：高衍生重力的精确等效性
A Tale of Two Butterflies: An Exact Equivalence in Higher-Derivative Gravity
论文作者
论文摘要
我们证明了高衍生理论中蝴蝶速度的两个全息计算与由曲率张量的任意收缩建立的Lagrangian的等效性。蝴蝶速度表征了混乱多体系统中局部扰动生长的速度，并且可以从超阶相关器中提取。这导致了全息计算，其中从双黑洞的地平线上的局部冲击波确定了蝴蝶速度。第二个全息计算使用纠缠楔重建来定义操作员大小的概念，并确定某些极端表面的蝴蝶速度。通过直接计算，我们表明，这两个蝴蝶速度在上述引力理论类别中恰好匹配。我们还提供了证据表明，这种等效性在所有引力理论中都存在。一路上，我们证明了冲击波空间的许多一般结果。
We prove the equivalence of two holographic computations of the butterfly velocity in higher-derivative theories with Lagrangian built from arbitrary contractions of curvature tensors. The butterfly velocity characterizes the speed at which local perturbations grow in chaotic many-body systems and can be extracted from the out-of-time-order correlator. This leads to a holographic computation in which the butterfly velocity is determined from a localized shockwave on the horizon of a dual black hole. A second holographic computation uses entanglement wedge reconstruction to define a notion of operator size and determines the butterfly velocity from certain extremal surfaces. By direct computation, we show that these two butterfly velocities match precisely in the aforementioned class of gravitational theories. We also present evidence showing that this equivalence holds in all gravitational theories. Along the way, we prove a number of general results on shockwave spacetimes.
