JT引力中的时空拓扑与几何：来自非交叉排列
Spacetime topology and geometry in JT Gravity from non-crossing permutations
- San José State University（圣何塞州立大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文通过非交叉排列的连续极限，将离散枚举参数映射为JT引力中的热边界长度和测地线长度，重现了低温行为及多边界配分函数，建立了与Weil-Petersson体积的直接联系。
AI中文摘要：
我们研究了如何将枚举非交叉排列的离散参数转化为JT引力中的几何量。通过分析圆盘上的非交叉排列以及两类环带非交叉排列，我们发现，在适当的连续标度极限下，标记边界点的数目变为热边界长度，而贯穿连接的数目变为测地线长度。在此极限下，这些枚举重现了圆盘上Schwarzian理论的普适低温行为，以及可定向和定向反转的双喇叭几何。随后，我们将这些构造与更高边界数的非交叉图联系起来，其连续枚举重现了通过将喇叭附着到亏格为零的Weil-Petersson体积的最高阶部分所得到的JT结果，这表明相同的喇叭-枚举参数映射可以推广到平面情形之外。综合来看，这些结果建立了非交叉排列枚举与附有喇叭的Weil-Petersson体积之间的直接联系，而这一构造在JT引力的引力路径积分中起着核心作用，并表明非交叉图为计算多边界配分函数提供了一条组合学途径。
英文摘要：
We study how discrete parameters which enumerate non-crossing permutations become geometric quantities in JT gravity. Analyzing non-crossing permutations on the disk together with two classes of annular non-crossing permutations, we find that under suitable continuum scaling limits the number of marked boundary points becomes the thermal boundary length, while the number of through-connections becomes a geodesic length. In this limit, the enumerations reproduce the universal low-temperature behavior of the Schwarzian theory on the disk and the orientable and orientation-reversing double-trumpet geometries. We then relate these constructions to higher-boundary non-crossing diagrams, whose continuum enumeration reproduces the JT result obtained by attaching trumpets to the top-degree part of genus-zero Weil-Petersson volumes, suggesting that the same trumpet--enumeration parameter mapping extends beyond the planar case. Together, these results establish a direct connection between non-crossing permutation enumerations and Weil-Petersson volumes with trumpets attached, a construction that plays a central role in the gravitational path integral in JT gravity, and suggest that non-crossing diagrams provide a combinatorial route to computing multi-boundary partition functions.
