龟兔赛跑：AdS/CFT中的因果谜题
The Tortoise and the Hare: A Causality Puzzle in AdS/CFT
AI总结：
针对AdS/CFT中体光速运动点可能导致边界子区域超光速的因果谜题，以AdS₃为例证明编码区域有限性可避免悖论，通过龟兔坐标测量编码非局域性，分析得零测地线存在临界编码刚好避免因果违反、其他编码为亚临界的结论。
摘要：
我们提出并解决了AdS/CFT中一个关于因果性明显违反的全息谜题。若AdS体中的一点以光速运动，编码它的边界子区域可能需要超光速运动才能跟上。以AdS₃为主要例子，我们证明编码区域的有限范围可避免悖论。我们发现最小尺寸编码区间的长度在AdS上产生了一个龟兔坐标，用于测量编码的非局域性。我们利用该坐标探索体中的圆周和径向运动，随后分析体零测地线。对于这些零测地线，总是存在临界编码，其中因果性的可能违反刚好被避免；我们证明在其他任何编码中，可能的违反都是亚临界的。
英文摘要：
We pose and resolve a holographic puzzle regarding an apparent violation of causality in AdS/CFT. If a point in the bulk of $AdS$ moves at the speed of light, the boundary subregion that encodes it may need to move superluminally to keep up. With $AdS_3$ as our main example, we prove that the finite extent of the encoding regions prevents a paradox. We show that the length of the minimal-size encoding interval gives rise to a tortoise coordinate on $\mathrm{AdS}$ that measures the nonlocality of the encoding. We use this coordinate to explore circular and radial motion in the bulk before passing to the analysis of bulk null geodesics. For these null geodesics, there is always a critical encoding where the possible violation of causality is barely avoided. We show that in any other encoding, the possible violation is subcritical.
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