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| Format: | Preprint |
| Publié: |
2025
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| Accès en ligne: | https://arxiv.org/abs/2509.20213 |
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| _version_ | 1866912792738529280 |
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| author | Orlov, A. Yu. |
| author_facet | Orlov, A. Yu. |
| 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 $SU(N)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_20213 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | SU(N) integrals and tau functions Orlov, A. Yu. Mathematical Physics 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 $SU(N)$. |
| title | SU(N) integrals and tau functions |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2509.20213 |