The central heat trace on large compact classical groups
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909898346856448 |
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| author | Lemoine, Thibaut Maïda, Mylène |
| author_facet | Lemoine, Thibaut Maïda, Mylène |
| contents | We establish the large-$N$ asymptotic expansion of the (central) trace of the heat kernel on any compact classical group $G_N\subset\mathrm{GL}_N(\mathbb{C})$, which extends a previous result known only for $\mathrm{U}(N)$ \cite{LM2}. It admits two new interpretations of the trace: in terms of ramified coverings of the torus, and Gromov-Witten invariants on elliptic curves. These connections allow us to explore several aspects of the gauge/string duality in two dimensions: a Yang-Mills/Hurwitz duality, and Yang-Mills/Gromov-Witten duality. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_08288 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The central heat trace on large compact classical groups Lemoine, Thibaut Maïda, Mylène Mathematical Physics Algebraic Geometry Combinatorics Probability Spectral Theory 05A17, 14H30, 43A75, 58J50 (primary), 81T13, 81T35 (secondary) We establish the large-$N$ asymptotic expansion of the (central) trace of the heat kernel on any compact classical group $G_N\subset\mathrm{GL}_N(\mathbb{C})$, which extends a previous result known only for $\mathrm{U}(N)$ \cite{LM2}. It admits two new interpretations of the trace: in terms of ramified coverings of the torus, and Gromov-Witten invariants on elliptic curves. These connections allow us to explore several aspects of the gauge/string duality in two dimensions: a Yang-Mills/Hurwitz duality, and Yang-Mills/Gromov-Witten duality. |
| title | The central heat trace on large compact classical groups |
| topic | Mathematical Physics Algebraic Geometry Combinatorics Probability Spectral Theory 05A17, 14H30, 43A75, 58J50 (primary), 81T13, 81T35 (secondary) |
| url | https://arxiv.org/abs/2511.08288 |