论文标题
在黑洞阈值下方没有合奏平均
No Ensemble Averaging Below the Black Hole Threshold
论文作者
论文摘要
在广告/CFT对应关系中，与连接的界限相关的散装歧管相关的幅度呈现出长期存在的谜团。一种可能的解释是，它们反映了边界理论合奏的平均效果。但是在尺寸$ d \ geq 3 $中的示例中，不存在适当的边界理论合奏。在这里，我们通过确定我们声称的一类“子阈值”可观察的物品来提高难题。这些是不涉及黑洞状态的幅度。为了支持我们的主张，我们探讨了$ d = 3 $的示例，并表明将爱因斯坦方程的解决方案与断开的边界连接起来永远不会导致亚阈值可观察到。为了证明这一点需要一些新的结果，这些结果涉及双曲线三序列的重新归一化体积，我们在双曲几何形状中使用现代方法证明了这一点。那么，为什么任何可观察到的东西都显示出明显的合奏平均呢？我们建议这反映了黑洞物理学的混乱性质以及描述黑洞的希尔伯特空间没有较大的$ n $限制的事实。
In the AdS/CFT correspondence, amplitudes associated to connected bulk manifolds with disconnected boundaries have presented a longstanding mystery. A possible interpretation is that they reflect the effects of averaging over an ensemble of boundary theories. But in examples in dimension $D\geq 3$, an appropriate ensemble of boundary theories does not exist. Here we sharpen the puzzle by identifying a class of "sub-threshold" observables that we claim do not show effects of ensemble averaging. These are amplitudes that do not involve black hole states. To support our claim, we explore the example of $D=3$, and show that connected solutions of Einstein's equations with disconnected boundary never contribute to sub-threshold observables. To demonstrate this requires some novel results about the renormalized volume of a hyperbolic three-manifold, which we prove using modern methods in hyperbolic geometry. Why then do any observables show apparent ensemble averaging? We propose that this reflects the chaotic nature of black hole physics and the fact that the Hilbert space describing a black hole does not have a large $N$ limit.
