arXiv 2201.119422022-01hep-th

JT引力和超引力的微观物理

The Microstate Physics of JT Gravity and Supergravity

Clifford V. Johnson

备注：: 54 pages, 39 multi-component figures, 8 tables, at least two puns, 1 trumpet. V2: Discussion clarified, sharpened, and otherwise improved. References added. Note added about a recent paper

摘要：

本文提出，要完全理解二维量子引力及其在随机矩阵模型中的出现，需要完全接受{ \it both} Wigner（统计学）和't Hooft（几何学）。使用随机矩阵模型的非微扰定义，产生各种JT重力和JT超重力模型的任意拓扑结构的欧几里德表面上，Fredholm行列式被用来提取精确的信息的光谱离散微观状态的物理基础。计算的一个核心结果是，在每种情况下，在首阶看到的（超）施瓦茨谱只是一种新的谱的近似，这种谱从根本上是离散的。进一步论证了矩阵模型指向表征洛伦兹（超）引力理论的全息对偶的离散谱的{ \it单一}独特的副本。这些事实表明，因式分解之谜完全解决了，因为作为史瓦西基础的离散谱可以在单个理论中有一个合理的量子力学起源，而不需要诉诸系综。有人认为，更一般地说，双尺度矩阵模型包含的信息都是关于量子引力的洛伦兹和欧几里得方法。前者来自Wignerian方法，后者来自t Hooftian 1/N拓扑展开。

英文摘要：

It is proposed that a complete understanding of two-dimensional quantum gravity and its emergence in random matrix models requires fully embracing {\it both} Wigner (statistics) and 't Hooft (geometry). Using non-perturbative definitions of random matrix models that yield various JT gravity and JT supergravity models on Euclidean surfaces of arbitrary topology, Fredholm determinants are used to extract precise information about the spectra of discrete microstates that underlie the physics. A core result of the computations is that in each case, the (super) Schwarzian spectrum seen at leading order is only an approximation to a new kind of spectrum that is fundamentally discrete. It is further argued that the matrix models point to a {\it single} distinguished copy of the discrete spectrum that characterizes the holographic dual of the Lorentzian (super) gravity theory. These facts suggest that the factorization puzzle is entirely resolved since the discrete spectrum underlying the Schwarzian can have a sensible quantum mechanical origin in a single theory, without an appeal to an ensemble. It is argued that more generally, double-scaled matrix models contain information about both the Lorentzian and Euclidean approaches to quantum gravity. The former comes from the Wignerian approach while the latter from the 't Hooftian 1/N topological expansion.

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英文摘要：

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