论文标题
重新归一化组方法，即具有首选叶片的量子重力基质模型的连续限制
Renormalization Group Approach to the Continuum Limit of Matrix Models of Quantum Gravity with Preferred Foliation
论文作者
论文摘要
这种贡献不是作为审查的目的，而是通过对编辑的建议，是瞥见量子重力的双重加权张量模型的领域。这类模型允许人们考虑更广泛的量子重力模型，特别是可以用固有的叶面概念来制定时空总和模型。这些模型中最简单的是Benedetti和Henson提出的模型，这是二维因果动力学三角剖分（CDT）的基质模型公式。在本文中，我们将功能性重归其化组方程（FRGE）应用于Benedetti-Henson模型，目的是研究此类模型的可能连续性限制。可能的连续限制出现在这种FRGE方法中，作为重新归一化组流的固定点，其中矩阵的大小充当重新归一化量表。考虑到非常小的截断，我们发现固定点与CDT的分析已知结果兼容二维。通过研究结果的方案依赖性，我们发现精确结果需要比本工作中考虑的更大的截断。我们得出的结论是，我们的工作表明，FRGE是用于双重加权矩阵模型的有用探索工具。因此，我们预计FRGE将是用于研究CDT的双重加权张量模型的有用探索工具。
This contribution is not intended as a review but, by suggestion of the editors, as a glimpse ahead into the realm of dually weighted tensor models for quantum gravity. This class of models allows one to consider a wider class of quantum gravity models, in particular one can formulate state sum models of spacetime with an intrinsic notion of foliation. The simplest one of these models is the one proposed by Benedetti and Henson, which is a matrix model formulation of two-dimensional Causal Dynamical Triangulations (CDT). In this paper we apply the Functional Renormalization Group Equation (FRGE) to the Benedetti-Henson model with the purpose of investigating the possible continuum limits of this class of models. Possible continuum limits appear in this FRGE approach as fixed points of the renormalization group flow where the size of the matrix acts as the renormalization scale. Considering very small truncations, we find fixed points that are compatible with analytically known results for CDT in two dimensions. By studying the scheme dependence of our results we find that precision results require larger truncations than the ones considered in the present work. We conclude that our work suggests that the FRGE is a useful exploratory tool for dually weighted matrix models. We thus expect that the FRGE will be a useful exploratory tool for the investigation of dually weighted tensor models for CDT in higher dimensions.
