量子引力中秩4张量场模型的非平凡UV行为
Nontrivial UV behavior of rank-4 tensor field models for quantum gravity
摘要：
利用泛函重整化群研究了秩为4的有色二分U（1）张量场模型在高斯不动点附近的普适类.在一个包含所有幂计数相关算子和边际算子的截断中，我们发现了一个与高斯不动点相连的一维UV吸引子。因此，这是第一个证据表明，该模型可能是渐近安全的，由于一个机制类似于在Grosse-Wulkenhaar模型中发现的一个，其UV行为附近的高斯不动点也描述了一维吸引子，其中包含高斯不动点。然而，负责β函数同时消失的抵消机制对于张量模型来说是新的，即它不会发生在矢量或矩阵模型中。
英文摘要：
We investigate the universality classes of rank-4 colored bipartite U(1) tensor field models near the Gaussian fixed point with the functional renormalization group. In a truncation that contains all power counting relevant and marginal operators, we find a one-dimensional UV attractor that is connected with the Gaussian fixed point. Hence this is first evidence that the model could be asymptotically safe due to a mechanism similar to the one found in the Grosse-Wulkenhaar model, whose UV behavior near the Gaussian fixed point is also described by one-dimensional attractor that contains the Gaussian fixed point. However, the cancellation mechanism that is responsible for the simultaneous vanishing of the beta functions is new to tensor models, i.e. it does not occur in vector or matrix models.
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