Fractal space-times under the microscope: a renormalization group view on Monte Carlo data
Fractal space-times under the microscope: a renormalization group view on Monte Carlo data
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DOI：
10.1007/jhep12(2011)012
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发表时间：
2011-12-01
影响因子：
5.4
通讯作者：
Saueressig, Frank
中科院分区：
文献类型：
--
作者：
Reuter, Martin;Saueressig, Frank
时空微观结构中分形特征的出现是许多量子引力方法的共同主题。本文对渐近安全量子爱因斯坦引力（QEG）的有效时空的谱维数d（s）和行走维数d（w）进行了详细的重整化群研究。我们发现了三种尺度机制，其中这些广义尺寸在扩展的长度尺度范围内近似恒定：经典机制，其中d（s）= d，d（w）= 2，半经典机制，其中d（s）= 2d/（2 + d），d（w）= 2 + d，以及UV固定点机制，其中d（s）= d/2，d（w）= 4。覆盖的三维蒙特卡罗模拟的长度尺度上，所得到的光谱尺寸被证明是非常好的协议与数据。这种比较也为因果动态三角剖分（CDT）、欧几里得动态三角剖分（EDT）和渐近安全性所报告的光谱维的短距离行为之间的明显困惑提供了一个自然的解释。
The emergence of fractal features in the microscopic structure of space-time is a common theme in many approaches to quantum gravity. In this work we carry out a detailed renormalization group study of the spectral dimension d(s) and walk dimension d(w) associated with the effective space-times of asymptotically safe Quantum Einstein Gravity (QEG). We discover three scaling regimes where these generalized dimensions are approximately constant for an extended range of length scales: a classical regime where d(s) = d, d(w) = 2, a semi-classical regime where d(s) = 2d/(2 + d), d(w) = 2 + d, and the UV-fixed point regime where d(s) = d/2, d(w) = 4. On the length scales covered by three-dimensional Monte Carlo simulations, the resulting spectral dimension is shown to be in very good agreement with the data. This comparison also provides a natural explanation for the apparent puzzle between the short distance behavior of the spectral dimension reported from Causal Dynamical Triangulations (CDT), Euclidean Dynamical Triangulations (EDT), and Asymptotic Safety.