Tau functions of the UC hierarchy as partition functions of matrix models
High Energy Physics - Theory
2025-12-02 v3 Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
Abstract
We present a family of matrix models such that their partition functions are tau functions of the universal character (UC) hierarchy. This develops one of the topics of our previous paper arXiv:2410.14823. We found new matrix models associated with the product of two spheres with embedded graphs via a gluing matrix. We also generalize these studies to multi-matrix models case, which corresponds to the multi-component UC hierarchy.
Cite
@article{arxiv.2506.12867,
title = {Tau functions of the UC hierarchy as partition functions of matrix models},
author = {Chuanzhong Li and Andrei Mironov and Alexander Yu. Orlov},
journal= {arXiv preprint arXiv:2506.12867},
year = {2025}
}
Comments
22 pages, 6 figures