Quantum chaotic systems are often defined via the assertion that their spectral statistics coincides with, or is well approximated by, random matrix theory. In this paper we explain how the universal content of random matrix theory emerges as the consequence of a simple symmetry-breaking principle and its associated Goldstone modes. This allows us to write down an effective-field theory (EFT) description of quantum chaotic systems, which is able to control the level statistics up to an accuracy ${\cal O} \left(e^{-S} \right)$ with $S$ the entropy. We explain how the EFT description emerges from explicit ensembles, using the example of a matrix model with arbitrary invariant potential, but also when and how it applies to individual quantum systems, without reference to an ensemble. Within AdS/CFT this gives a general framework to express correlations between "different universes" and we explicitly demonstrate the bulk realization of the EFT in minimal string theory where the Goldstone modes are bound states of strings stretching between bulk spectral branes. We discuss the construction of the EFT of quantum chaos also in higher dimensional field theories, as applicable for example for higher-dimensional AdS/CFT dual pairs.

中文翻译：

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全息量子混沌的后期物理学

量子混沌系统通常通过以下断言来定义：它们的光谱统计与随机矩阵理论一致或近似。在本文中，我们解释了随机矩阵理论的通用内容是如何作为简单的对称破缺原理及其相关的戈德斯通模式的结果而出现的。这使我们能够写下量子混沌系统的有效场论 (EFT) 描述，它能够控制水平统计达到精度 ${\cal O} \left(e^{-S} \right) $ 和 $S$ 是熵。我们解释了 EFT 描述如何从显式集成中出现，使用具有任意不变势的矩阵模型的例子，以及它何时以及如何应用于单个量子系统，而不参考集成。在 AdS/CFT 中，这给出了表达“不同宇宙”之间相关性的一般框架，我们明确地证明了 EFT 在最小弦理论中的批量实现，其中戈德斯通模式是在体谱膜之间拉伸的弦的束缚状态。我们还在高维场论中讨论了量子混沌 EFT 的构造，例如适用于高维 AdS/CFT 双对。