High Energy Physics - Theory
[Submitted on 13 Apr 2022 (v1), last revised 3 Aug 2022 (this version, v3)]
Title:Kazakov-Migdal model on the Graph and Ihara Zeta Function
View PDFAbstract: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.
Submission history
From: Kazutoshi Ohta [view email][v1] Wed, 13 Apr 2022 14:37:53 UTC (5,770 KB)
[v2] Tue, 10 May 2022 13:03:09 UTC (5,771 KB)
[v3] Wed, 3 Aug 2022 08:20:18 UTC (6,899 KB)
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