Dynkin diagrams, generalized Nahm sums and 2d CFTs
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2026
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| _version_ | 1866911559867957248 |
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| author | Sun, Kaiwen Wang, Haowu |
| author_facet | Sun, Kaiwen Wang, Haowu |
| contents | A folklore conjecture states that the Nahm sum associated with a pair of Dynkin diagrams of type $ADET$ is a modular function. In this paper, we extend this conjecture to Dynkin diagrams of type $ABCDEFGT$ in the context of generalized Nahm sums. The modular Nahm sums are closely related to the characters of 2d rational conformal field theories. In this work, we identify many specific generalized Nahm sums with characters of some well-studied 2d CFTs. For example, we find that the generalized Nahm sums associated with $(T_1, C_r)$ and $(T_1,D_r)$ correspond to the supersymmetric Virasoro minimal models $\mathrm{SM}(4r+6, 4)$ and $\mathrm{SM}(8r+4, 2)$, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_00847 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Dynkin diagrams, generalized Nahm sums and 2d CFTs Sun, Kaiwen Wang, Haowu Mathematical Physics High Energy Physics - Theory Combinatorics Number Theory A folklore conjecture states that the Nahm sum associated with a pair of Dynkin diagrams of type $ADET$ is a modular function. In this paper, we extend this conjecture to Dynkin diagrams of type $ABCDEFGT$ in the context of generalized Nahm sums. The modular Nahm sums are closely related to the characters of 2d rational conformal field theories. In this work, we identify many specific generalized Nahm sums with characters of some well-studied 2d CFTs. For example, we find that the generalized Nahm sums associated with $(T_1, C_r)$ and $(T_1,D_r)$ correspond to the supersymmetric Virasoro minimal models $\mathrm{SM}(4r+6, 4)$ and $\mathrm{SM}(8r+4, 2)$, respectively. |
| title | Dynkin diagrams, generalized Nahm sums and 2d CFTs |
| topic | Mathematical Physics High Energy Physics - Theory Combinatorics Number Theory |
| url | https://arxiv.org/abs/2604.00847 |