论文标题

复兴的Stokes painleve方程和二维量子(超级)重力的数据

Resurgent Stokes Data for Painleve Equations and Two-Dimensional Quantum (Super) Gravity

论文作者

Baldino, Salvatore, Schiappa, Ricardo, Schwick, Maximilian, Vega, Roberto

论文摘要

可以通过这些非线性差分方程来递归地构建到帕克雷维方程的复兴 - 透射式解决方案 - 但要求在复杂平面上全球定义的Stokes数据。 Stokes数据明确构建了连接形式,该数据通过实施作用于跨系列的Stokes转变来描述与这些解决方案相关的非线性Stokes现象。但是,非线性复苏stokes数据缺乏,但是,第一原理计算方法很难一般确定。在Painleve I和Painleve II环境中,由于这些方程是谐音,因此非线性Stokes数据受到了进一步的阻碍,对跨系列扇区,桥式方程和相关Stokes系数之间的互连产生了非平凡的后果。与此同时,Painleve I和Painleve II方程是二维量子(超级)重力和最小弦理论的弦乐,其中Stokes数据具有自然的ZZ-Brane解释。这项工作首次计算完整的,分析的,复兴的Stok,以及其量子重力或最小的字符串化身以及它们的量子重力。本文开发的方法被称为“闭合形式渐近学”,唯一地利用了复兴的跨系列解决方案的大型渐近造型 - 仔细分析了角色共振的作用。鉴于其普遍性,它可能适用于其他不同(非线性,共振)问题。分析性Stokes系数的结果具有自然结构,这些结构被描述为自然结构,广泛的高精度数值测试证实了所有分析预测。明确构建了连接形式,并具有编码完整的Stokes数据的相当简单,紧凑的最终结果,并进一步允许进行精确的单肌检查 - 因此,为我们的结果提供了分析证明。

Resurgent-transseries solutions to Painleve equations may be recursively constructed out of these nonlinear differential-equations -- but require Stokes data to be globally defined over the complex plane. Stokes data explicitly construct connection-formulae which describe the nonlinear Stokes phenomena associated to these solutions, via implementation of Stokes transitions acting on the transseries. Nonlinear resurgent Stokes data lack, however, a first-principle computational approach, hence are hard to determine generically. In the Painleve I and Painleve II contexts, nonlinear Stokes data get further hindered as these equations are resonant, with non-trivial consequences for the interconnections between transseries sectors, bridge equations, and associated Stokes coefficients. In parallel to this, the Painleve I and Painleve II equations are string-equations for two-dimensional quantum (super) gravity and minimal string theories, where Stokes data have natural ZZ-brane interpretations. This work computes for the first time the complete, analytical, resurgent Stokes data for the first two Painleve equations, alongside their quantum gravity or minimal string incarnations. The method developed herein, dubbed "closed-form asymptotics", makes sole use of resurgent large-order asymptotics of transseries solutions -- alongside a careful analysis of the role resonance plays. Given its generality, it may be applicable to other distinct (nonlinear, resonant) problems. Results for analytical Stokes coefficients have natural structures, which are described, and extensive high-precision numerical tests corroborate all analytical predictions. Connection-formulae are explicitly constructed, with rather simple and compact final results encoding the full Stokes data, and further allowing for exact monodromy checks -- hence for an analytical proof of our results.

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