论文标题
最低统一SL（2，c）不变的渐近学
Asymptotics of lowest unitary SL(2,C) invariants on graphs
论文作者
论文摘要
我们描述了一种研究与图形相关的SL（2，c）不变张量的渐近学技术，带有单一的无用和最低的SU（2）旋转，并将其应用于Lorentzian Eprl-Kkl（Engle，Pereira，Pereira，Pereira，Rovelli，Rovelli，Rovelli，livine，livine; Kaminski; Kaminski，Kieselowski，lelowski，le lewandoski）模型。我们在几何变量上重现了4-Simplex图的已知渐近学，并具有不同的视角，并引入了对任何图的有效的算法。从一般来看，我们发现关键配置不仅是恢复几何形状，而且是对应于保形扭曲几何形状的较大集合。这些可以是欧几里得或洛伦兹，并将弯曲和扁平的4D多型作为亚集。对于模块化图，我们表明存在多对关键点，并且在不同的子图中存在混合签名，欧几里得和洛伦兹的关键配置，而没有4D嵌入。
We describe a technique to study the asymptotics of SL(2,C) invariant tensors associated to graphs, with unitary irreps and lowest SU(2) spins, and apply it to the Lorentzian EPRL-KKL (Engle, Pereira, Rovelli, Livine; Kaminski, Kieselowski, Lewandowski) model of quantum gravity. We reproduce the known asymptotics of the 4-simplex graph with a different perspective on the geometric variables and introduce an algorithm valid for any graph. On general grounds, we find that critical configurations are not just Regge geometries, but a larger set corresponding to conformal twisted geometries. These can be either Euclidean or Lorentzian, and include curved and flat 4d polytopes as subsets. For modular graphs, we show that multiple pairs of critical points exist, and there exist critical configurations of mixed signature, Euclidean and Lorentzian in different subgraphs, with no 4d embedding possible.
