论文标题
随机随机矩阵的新兴量子几何形状
Emergent quantum geometry from stochastic random matrices
论文作者
论文摘要
为了制定量子重力，我们提出了一种新的机制，可以从随机性出现时空几何形状。在[Arxiv：1705.06097]中，我们为给定的Markov随机过程定义了“配置之间的距离”，该过程列举了配置之间的过渡难度。在本文中，我们考虑了大型矩阵模型的随机过程，我们将特征值视为时空坐标。我们研究了一个元素价值的有效随机过程的距离，并认为可以在非批评弦理论中解释该距离为用d-instanton探测经典的几何形状。我们进一步提供了证据表明，当我们将形式主义应用于$ u（n）$矩阵的脾气紧密的过程时，'t Hooft耦合被视为另一个动力学变量时，欧几里得ads $ _2 $ geometry在大型$ n $ lippitions the Horizon senfortions the Gross shipertitions the Gross-wia-wia-wia-wia-wadia-wadia-waddia-ward-waddia-waddia-waddia-ward-waddia termitive in the Extended配置中出现。
Towards formulating quantum gravity, we present a novel mechanism for the emergence of spacetime geometry from randomness. In [arXiv:1705.06097], we defined for a given Markov stochastic process "the distance between configurations," which enumerates the difficulty of transition between configurations. In this article, we consider stochastic processes of large-$N$ matrix models, where we regard the eigenvalues as spacetime coordinates. We investigate the distance for the effective stochastic process of one-eigenvalue, and argue that this distance can be interpreted in noncritical string theory as probing a classical geometry with a D-instanton. We further give an evidence that, when we apply our formalism to a tempered stochastic process of $U(N)$ matrix, where the 't Hooft coupling is treated as another dynamical variable, a Euclidean AdS$_2$ geometry emerges in the extended configuration space in the large-$N$ limit, and the horizon corresponds to the Gross-Witten-Wadia phase transition point.
