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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.20213 |
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Table of Contents:
- We present a family of solvable multi-matrix models associated with an arbitrary embedded graph $Γ$ with a single vertex. The graph with $n$ edges is equipped with $2n$ corner matrices. The partition function of each member of the family depends on the set of eigenvalues of monodromies of corner matrices around the vertices of the dual graph $Γ^*$ and sets of parameters attached to each vertex of $Γ$. We select the cases where the partition function of a model is a tau function of KP, 2KP and BKP hiearachies. We compare integrals over ${U}(N)$ and over ${SU}(N)$ groups. In $U(N)$ case there is no restriction on the number of vertices of $Γ$. We also consider mixed ensembles of matrices from $GL(N),U(N)$ and $SU(N)$.