English

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.

Keywords

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