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arXiv 2005.01893hep-thgr-qc
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JT超引力、最小弦和矩阵模型

JT Supergravity, Minimal Strings, and Matrix Models

Clifford V. Johnson

备注：
15 pages, 9 multi-component figures, 1 trumpet v2: Discussion of perturbation theory improved. Overall presentation enhanced in various places
发表信息：
Phys. Rev. D 103, 046012 (2021)
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摘要：

本文提出，最近由Stanford和Witten结合矩阵模型讨论的一类Jackiw-Teitelboim超引力子族，可以用最小弦论的一个特定组合给出拓扑展开及其以外的所有阶的完整定义。这种结构定义了超引力的非微扰物理学，它是明确的和稳定的。极小模型来自双尺度复杂矩阵模型，并且对应于随机矩阵集合的Altland-Zirnbauer $(\boldsymbolα,\boldsymbolβ)$分类中的情况$(2Γ{+}1,2)$，其中$Γ$是参数。一个中心的作用是由一个非线性的“弦方程”，它自然地包含了$Γ$，通常被认为是一个整数，例如，极小模型中的D-膜。这里，半整数$Γ$也有一个解释。事实上，$Γ{=}{\pm}\frac12$产生了由Stanford和Witten证明具有非常特殊性质的情形$(0,2)$和$(2,2)$。这些特征在这个定义中很明显，因为弦方程的相关解对于$Γ{=}{\pm}\frac12$具有特殊的性质。其他半整数$Γ$的额外特殊特征表明超重力模型中有新的惊喜。

英文摘要：

It is proposed that a family of Jackiw-Teitelboim supergravites, recently discussed in connection with matrix models by Stanford and Witten, can be given a complete definition, to all orders in the topological expansion and beyond, in terms of a specific combination of minimal string theories. This construction defines non-perturbative physics for the supergravity that is well-defined and stable. The minimal models come from double-scaled complex matrix models and correspond to the cases $(2Γ{+}1,2)$ in the Altland-Zirnbauer $(\boldsymbolα,\boldsymbolβ)$ classification of random matrix ensembles, where $Γ$ is a parameter. A central role is played by a non-linear `string equation' that naturally incorporates $Γ$, usually taken to be an integer, counting e.g., D-branes in the minimal models. Here, half-integer $Γ$ also has an interpretation. In fact, $Γ{=}{\pm}\frac12$ yields the cases $(0,2)$ and $(2,2)$ that were shown by Stanford and Witten to have very special properties. These features are manifest in this definition because the relevant solutions of the string equation have special properties for $Γ{=}{\pm}\frac12$. Additional special features for other half-integer $Γ$ suggest new surprises in the supergravity models.

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