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arXiv 2108.11409hep-thgr-qcmath-phmath.MPnlin.SI
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从极小弦走向 Jackiw-Teitelboim 引力：论其 Resurgence、共振与黑洞

From Minimal Strings towards Jackiw-Teitelboim Gravity: On their Resurgence, Resonance, and Black Holes

Paolo Gregori, Ricardo Schiappa

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107 pages, 50 plots in 25 figures, 2 tables, jheppub-nosort.sty; v2: minor corrections/typos
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AI总结：

本文在矩阵模型框架下精确研究极小弦到 JT 引力的大物质中心荷极限，通过谱几何和弦方程在微扰与非微扰层面分析其 resurgent 结构、共振现象及黑洞微扰。

摘要：

最近揭示了 JT 二维 dilaton-引力有两个显著事实：该理论对偶于一个量子力学理论的系综；并且这种系综由一个随机矩阵模型描述，而该随机矩阵模型本身可被视为极小弦理论的一个特殊（大物质中心荷）极限。本工作处理这一极限，将其置于更广泛的矩阵模型背景中；比较多临界模型与极小弦之间的结果（即在多临界背景与共形背景之间进行切换）；并在两种情形下使大物质中心荷极限变得精确（因为这种极限也可以为多临界序列定义）。这些分析首先通过谱几何进行，在微扰和非微扰两个层面上，处理微扰理论的 resurgent 大阶增长，同时计算非微扰瞬子作用量和相应的 Stokes 数据。这一计算需要一种能够达到大阶的算法，该算法对任意二维拓扑引力都有效。弦方程——由 resolvent 的 GD 构造导出——在多临界和极小弦理论两种背景下被分析，并在微扰和非微扰两个层面进行研究（始终与先前的谱几何计算相匹配）。所得解由 resurgent transseries 描述，并被证明是共振的。大物质中心荷极限在弦方程背景下被处理，特别是，JT 引力的弦方程被推进到已知的零亏格情形之外的更高导数阶（其可能的精确形式也被讨论）。最后，包括了对这些极小弦模型中 Schwarzschild 型黑洞解的引力微扰的讨论——将其视为 JT 引力的形变——并简要讨论了 quasinormal modes。

英文摘要：

Two remarkable facts about JT two-dimensional dilaton-gravity have been recently uncovered: this theory is dual to an ensemble of quantum mechanical theories; and such ensemble is described by a random matrix model which itself may be regarded as a special (large matter-central-charge) limit of minimal string theory. This work addresses this limit, putting it in its broader matrix-model context; comparing results between multicritical models and minimal strings (i.e., changing in-between multicritical and conformal backgrounds); and in both cases making the limit of large matter-central-charge precise (as such limit can also be defined for the multicritical series). These analyses are first done via spectral geometry, at both perturbative and nonperturbative levels, addressing the resurgent large-order growth of perturbation theory, alongside a calculation of nonperturbative instanton-actions and corresponding Stokes data. This calculation requires an algorithm to reach large-order, which is valid for arbitrary two-dimensional topological gravity. String equations -- as derived from the GD construction of the resolvent -- are analyzed in both multicritical and minimal string theoretic contexts, and studied both perturbatively and nonperturbatively (always matching against the earlier spectral-geometry computations). The resulting solutions, as described by resurgent transseries, are shown to be resonant. The large matter-central-charge limit is addressed -- in the string-equation context -- and, in particular, the string equation for JT gravity is obtained to next derivative-orders, beyond the known genus-zero case (its possible exact-form is also discussed). Finally, a discussion of gravitational perturbations to Schwarzschild-like black hole solutions in these minimal-string models, regarded as deformations of JT gravity, is included - alongside a brief discussion of quasinormal modes.

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