Kazakov-Migdal model on the graph and Ihara zeta function

Journal of High Energy Physics

Regular Article - Theoretical Physics

So Matsuura¹  Kazutoshi Ohta² 

[1] Hiyoshi Departments of Physics and Research and Education Center for Natural Sciences, Keio University, 4-1-1 Hiyoshi, 223-8521, Yokohama, Kanagawa, Japan;Institute of Physics, Meiji Gakuin University, 244-8539, Yokohama, Kanagawa, Japan;

关键词: Lattice Integrable Models;    Lattice Quantum Field Theory;    Matrix Models;    Lattice QCD;   

DOI  :  10.1007/JHEP09(2022)178

 received in 2022-08-04, accepted in 2022-09-07,  发布年份 2022

来源: Springer

【 摘 要 】

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.

【 授权许可】

Unknown   
© The Author(s) 2022