两只蝴蝶的故事：高阶导数引力的精确等价
A Tale of Two Butterflies: An Exact Equivalence in Higher-Derivative Gravity
摘要：
我们证明了两个全息计算的蝴蝶速度在高阶导数理论与拉格朗日建立从任意收缩的曲率张量的等价性。蝴蝶速度表征了混沌多体系统中局部扰动增长的速度，可以从无序相关器中提取。这就引出了一种全息计算，其中蝴蝶的速度是由双黑洞视界上的局部冲击波确定的。第二个全息计算使用纠缠楔重建来定义算子大小的概念，并从某些极值表面确定蝴蝶速度。通过直接计算，我们证明了这两个蝴蝶速度在上述引力理论中精确匹配。我们还提出证据表明，这种等价性在所有引力理论中成立。一路上，我们证明了一些一般结果的冲击波时空。
英文摘要：
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.
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