论文标题
图和Ihara Zeta功能上的Kazakov-Migdal模型
Kazakov-Migdal model on the Graph and Ihara Zeta Function
论文作者
论文摘要
我们在图上提出了Kazakov-Migdal模型，并表明，当对该模型的参数进行适当调整时，分区函数由扩展的Ihara Zeta函数的单一矩阵积分表示，该函数的整个Ihara Zeta函数具有串联的扩展，由所有非collapsing Wilson loops at lengums as a strughs as a st ravess as as a s strupss。该模型的分区函数根据集成顺序以两种不同的方式表示。由于这种双重性，可以在任何有限的$ n $上执行特定的统一矩阵积分。我们精确地评估了大型$ n $限制中的任意图上的参数调整的Kazakov-Migdal模型的分区函数，并表明该图是该图的Ihara Zeta函数的无限乘积表示。
We propose the Kazakov-Migdal model on graphs and show that, when the parameters of this model are appropriately tuned, the partition function is represented by the unitary matrix integral of an extended Ihara zeta function, which has a series expansion by all non-collapsing Wilson loops with their lengths as weights. The partition function of the model is expressed in two different ways according to the order of integration. A specific unitary matrix integral can be performed at any finite $N$ thanks to this duality. We exactly evaluate the partition function of the parameter-tuned Kazakov-Migdal model on an arbitrary graph in the large $N$ limit and show that it is expressed by the infinite product of the Ihara zeta functions of the graph.
