arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2204.07583hep-thcond-mat.str-elnlin.CD
收藏

二维引力中的量子混沌

Quantum chaos in 2D gravity

Alexander Altland, Boris Post, Julian Sonner, Jeremy van der Heijden, Erik Verlinde

备注：
49 pages, 2 appendices, 9 figures; v3: rewrote introduction, simplified Fig. 1
发表信息：
SciPost Phys. 15, 064 (2023)
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

AI总结：

本文通过宇宙场论和味矩阵理论，在二维引力中给出了量子混沌遍历相的完全非微扰描述，并用 D-膜真空几何解释了因果对称性的破缺与恢复。

摘要：

我们在二维引力背景下，对量子混沌的遍历相给出了一个定量的、完全非微扰的描述。为此，我们通过其关联的宇宙场论来描述半经典二维引力的双重非微扰完备化。我们分析的核心指导原则是用味矩阵理论（fMT）来描述全息引力的遍历相，该理论展现出 U(n|n) 因果对称性的破缺与恢复。单独的 JT 引力及其二维引力近亲并不能实现具有因果对称性的作用量原理，但我们证明它们的宇宙场论，即 Kodaira-Spencer（KS）引力理论，确实可以实现。在直接从 KS 理论中的膜-反膜关联子推导出 fMT 之后，我们证明因果对称性的破缺与恢复可以从几何上理解为不同的（拓扑）D-膜真空。我们用全纯 Chern-Simons 理论与其闭弦等价理论，即 KS 引力理论之间的开闭弦对偶来解释我们的结果。重点将放在把这些几何原理与量子遍历相的特征谱关联联系起来。

英文摘要：

We present a quantitative and fully non-perturbative description of the ergodic phase of quantum chaos in the setting of two-dimensional gravity. To this end we describe the doubly non-perturbative completion of semiclassical 2D gravity in terms of its associated universe field theory. The guiding principle of our analysis is a flavor-matrix theory (fMT) description of the ergodic phase of holographic gravity, which exhibits $\mathrm{U}(n|n)$ causal symmetry breaking and restoration. JT gravity and its 2D-gravity cousins alone do not realize an action principle with causal symmetry, however we demonstrate that their {\it universe field theory}, the Kodaira-Spencer (KS) theory of gravity, does. After directly deriving the fMT from brane-antibrane correlators in KS theory, we show that causal symmetry breaking and restoration can be understood geometrically in terms of different (topological) D-brane vacua. We interpret our results in terms of an open-closed string duality between holomorphic Chern-Simons theory and its closed-string equivalent, the KS theory of gravity. Emphasis will be put on relating these geometric principles to the characteristic spectral correlations of the quantum ergodic phase.

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。

↑