Title:
Graph Zeta Functions and Wilson Loops in Kazakov-Migdal Model

Abstract:
We consider a generalized Kazakov-Migdal model defined on an arbitrary graph. The partition function of the model can be represented by the unitary matrix integral of the weighted graph zeta functions, which have series expansions by possible Wilson loops (graph cycles). The partition function of the model has two different expressions (dual pictures) according to the order of integration and can be evaluated exactly for some graphs thanks to this duality. On the other hand, we exactly evaluate the partition function of the Kazakov-Migdal model on the graph in the large N limit and show that it is expressed by the infinite product of the graph zeta functions. We also discuss the relation to the random matrix model approach.

This talk is based on arXiv:2204.06424 and arXiv:2208.14032.