量子群自旋网：精化极限及其与自旋泡沫的关系
Quantum group spin nets: refinement limit and relation to spin foams
摘要：
到目前为止，自旋泡沫模型除了一些基本的构建模块外，几乎没有被理解。为了在这个问题上取得进展，我们定义了类似的自旋泡沫模型，所谓的自旋网，量子群$\text{SU}(2)_k$和检查其有效的连续动力学通过张量网络重整化。在这种粗粒化过程的细化极限，我们发现了一个巨大的非平凡的不动点结构以外的退化和$BF$阶段。与以前的工作相比，我们使用不动点交织器，灵感来自Reisenberger的构造原理[1]和最近的工作[2]，作为初始参数化。在这个新的参数化微调是不需要的，以流到这些新的固定点。令人鼓舞的是，每个固定点都有一个相关联的扩展阶段，这使得在未来的相变的研究。最后，我们还提出了一个解释的自旋网的melonic自旋泡沫。因此，自旋网的粗粒化流可以被解释为描述两个自旋泡沫顶点或时空原子之间的有效耦合。
英文摘要：
So far spin foam models are hardly understood beyond a few of their basic building blocks. To make progress on this question, we define analogue spin foam models, so called spin nets, for quantum groups $\text{SU}(2)_k$ and examine their effective continuum dynamics via tensor network renormalization. In the refinement limit of this coarse graining procedure, we find a vast non-trivial fixed point structure beyond the degenerate and the $BF$ phase. In comparison to previous work, we use fixed point intertwiners, inspired by Reisenberger's construction principle [1] and the recent work [2], as the initial parametrization. In this new parametrization fine tuning is not required in order to flow to these new fixed points. Encouragingly, each fixed point has an associated extended phase, which allows for the study of phase transitions in the future. Finally we also present an interpretation of spin nets in terms of melonic spin foams. The coarse graining flow of spin nets can thus be interpreted as describing the effective coupling between two spin foam vertices or space time atoms.
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