Kazakov-Migdal model on the graph and Ihara zeta function

So Matsuura, Kazutoshi Ohta

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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.

Original languageEnglish
Article number178
JournalJournal of High Energy Physics
Issue number9
Publication statusPublished - 2022 Sept


  • Lattice Integrable Models
  • Lattice QCD
  • Lattice Quantum Field Theory
  • Matrix Models

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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