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arXiv 2403.08696hep-thgr-qc
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关于JT引力的非微扰体希尔伯特空间

On the non-perturbative bulk Hilbert space of JT gravity

Luca V. Iliesiu, Adam Levine, Henry W. Lin, Henry Maxfield, Márk Mezei

备注：
67 pages + appendices + 16 overcomplete figures, v2, v3: added references + minor improvements
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AI总结：

本文在二维JT引力中通过度规变量显式定义了非微扰体希尔伯特空间，识别零态并研究两个体算符的非微扰行为，结果表明晚期探测到火墙的概率为O(1)且自平均普适。

摘要：

量子引力的体希尔伯特空间是什么？在本文中，我们在二维JT引力中解决了这一问题，包括有物质和无物质的情况，给出了一个以度规变量明确指定的非微扰希尔伯特空间的显式定义。这些态是长度和物质态的波函数，但具有非平凡且高度简并的内积。我们明确识别了零态，并讨论了它们对于非微扰地定义算符的重要性。为了突出我们所发展的形式体系的威力，我们研究了两个体线性算符的非微扰效应，这两个算符可以作为观测者落入双侧黑洞体验的代理：一个捕捉爱因斯坦-罗森桥的长度，另一个捕捉从相反两侧落入的两个粒子之间的质心碰撞能量。我们追踪这些算符的行为直到时间量级为$e^{S_\ ext{BH}}$，此时波函数扩散到这些算符的完备本征态集合。如果这些可观测量确实是落入观测者体验的良好代理，我们的结果表明在晚期探测到火墙的概率为O(1)，且该概率是自平均和普适的。

英文摘要：

What is the bulk Hilbert space of quantum gravity? In this paper, we resolve this problem in 2d JT gravity, both with and without matter, providing an explicit definition of a non-perturbative Hilbert space specified in terms of metric variables. The states are wavefunctions of the length and matter state, but with a non-trivial and highly degenerate inner product. We explicitly identify the null states, and discuss their importance for defining operators non-perturbatively. To highlight the power of the formalism we developed, we study the non-perturbative effects for two bulk linear operators that may serve as proxies for the experience of an observer falling into a two-sided black hole: one captures the length of an Einstein-Rosen bridge and the other captures the center-of-mass collision energy between two particles falling from opposite sides. We track the behavior of these operators up to times of order $e^{S_\text{BH}}$, at which point the wavefunction spreads to the complete set of eigenstates of these operators. If these observables are indeed good proxies for the experience of an infalling observer, our results indicate an O(1) probability of detecting a firewall at late times that is self-averaging and universal.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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