随机矩阵的涌现量子几何
Emergent quantum geometry from stochastic random matrices
摘要：
为了建立量子引力，我们提出了一种时空几何从随机性中出现的新机制。在[arXiv：1705.06097]中，我们为给定的马尔可夫随机过程定义了“配置之间的距离”，它列举了配置之间转换的难度。本文考虑大- $N$矩阵模型的随机过程，其中把特征值看作时空坐标。我们研究了单本征值有效随机过程的距离，并认为这个距离可以在非临界弦论中解释为用D-瞬子探测经典几何。我们进一步证明，当我们将我们的形式应用于$U(N)$矩阵的回火随机过程时，其中t Hooft耦合被视为另一个动力学变量，在大- $N$极限下，在扩展的位形空间中出现一个Euclidean AdS $_2$几何，视界对应于Gross-Witten-Wadia相变点.
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
