JT引力中婴儿宇宙效应会导致什么？——用三种方法分析晚时关联函数与ERB长度——
What happens due to the baby universe effect in JT gravity? -Analysis of correlation functions and ERB length at late time using three approaches-
AI总结：
本文用测地线求和、无捷径模空间积分和普适谱密度关联三种方法，揭示JT引力晚时斜坡、平台及ERB长度三次增长后饱和的婴儿宇宙效应。
摘要：
我们使用三种方法分析JT引力中的关联函数：对连接边界算符的所有测地线求和，在由D. Stanford和Z. Yang提出的“无捷径条件”所确定的模空间区域上积分，以及使用τ标度极限下的普适谱密度关联公式。我们发现三种结果在晚时的行为一致：它们都呈现“斜坡”，而非永久衰减。利用第三种方法，我们还确认在T_H=2πe^{S_0}\hatρ_0(E)之后出现“平台”。总体而言，我们的结果与SFF分析一致。我们还用这三种方法计算了ERB长度⟨ℓ(T)⟩，发现结果彼此高度吻合。我们还发现，由于包含一个可观测婴儿宇宙的几何贡献，⟨ℓ(T)⟩随T呈三次函数增长，并在T=T_H之后收敛到常数。对于含一个婴儿宇宙的几何，我们计算了婴儿宇宙的尺寸⟨b(T)⟩，发现它与⟨ℓ(T)⟩同阶。该结果与P. Saad所主张的婴儿宇宙发射机制一致。
英文摘要：
We analyze the correlation function in JT gravity using three approaches: by summing over all geodesics connecting boundary operators, integrating over the region of moduli space determined by the ``no-shortcut condition'' introduced by D.Stanford and Z.Yang, and using the formula for the universal spectral density correlation in the $τ$-scaling limit. We find that the behaviors of the three results coincide at late times: they all exhibit a ``ramp'' instead of permanent decay. Using the third approach we also confirm that the ``plateau'' appears after $T_H=2πe^{S_0}\hatρ_0(E)$. Overall, our results are consistent with the SFF analysis. We also calculate the ERB length $\langle \ell(T) \rangle$ using the three approaches and find that the results are in good agreement with each other. We also find that the $\langle \ell(T) \rangle$ grows as a cubic function in $T$ due to the contribution from geometry including one observable baby universe, and converges to a constant after $T=T_H$. For the geometry with one baby universe, we compute the size $\langle b(T) \rangle$ of the baby universe and find that it is of the same order as $\langle \ell(T) \rangle$. This result is consistent with the baby universe emission mechanism claimed by P.Saad.
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