Tau functions of the UC hierarchy as partition functions of matrix models

2025/06/15 by Li, Chuanzhong, Mironov, Andrei, Orlov, Alexander Yu.
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2506.12867

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.

Citations

• Coupling of different solvable ensembles of random matrices
• New Insights into Superintegrability from Unitary Matrix Models
• Hurwitz numbers from matrix integrals over Gaussian measure
• Integrals of tau functions
• UC hierarchy and monodromy preserving deformation
• From KP/UC hierarchies to Painleve equations
• Random Matrices
• New Solvable Matrix Integrals
• Solvable Matrix Models
• Conformal Field Theory Techniques in Random Matrix models
• Generalized Hirota Equations in Models of 2D Quantum Gravity

Related

• Matrix models for the nested hypergeometric tau-functions
• Tau functions of the constrained matrix KP hierarchy
• Hermitian One-Matrix Model and KP Hierarchy
• Series over fat partitions: matrix models and discrete ensembles
• SU(N) integrals and tau functions