TY - JOUR

T1 - Kazakov-Migdal model on the graph and Ihara zeta function

AU - Matsuura, So

AU - Ohta, Kazutoshi

N1 - Publisher Copyright:
© 2022, The Author(s).

PY - 2022/9

Y1 - 2022/9

N2 - 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.

AB - 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.

KW - Lattice Integrable Models

KW - Lattice QCD

KW - Lattice Quantum Field Theory

KW - Matrix Models

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U2 - 10.1007/JHEP09(2022)178

DO - 10.1007/JHEP09(2022)178

M3 - Article

AN - SCOPUS:85138565024

SN - 1126-6708

VL - 2022

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 9

M1 - 178

ER -