Four-dimensional random geometries can be generated by statistical models with rank-4 tensors as random variables. These are dual to discrete building blocks of random geometries. We discover a potential candidate for a continuum limit in such a model by employing background-independent coarse-graining techniques where the tensor size serves as a pre-geometric notion of scale. A fixed point candidate which features two relevant directions is found. The possible relevance of this result in view of universal results for quantum gravity and a potential connection to the asymptotic-safety program is discussed.

中文翻译：

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四维量子引力张量模型中的普遍临界行为

四维随机几何可以通过统计模型以 4 阶张量作为随机变量生成。这些是随机几何结构的双重到离散构建块。我们通过采用与背景无关的粗粒度技术，在这种模型中发现了连续统极限的潜在候选者，其中张量大小作为尺度的前几何概念。找到具有两个相关方向的固定点候选。鉴于量子引力的普遍结果以及与渐近安全程序的潜在联系，讨论了该结果的可能相关性。