Periodic -Systems and Nahm Sums: The Rank 2 Case
We classify periodic -systems of rank 2 satisfying the symplectic property. We find that there are six such -systems. In all cases, the periodicity follows from the existence of two reddening sequences associated with the time evolution of the -systems in positive and negative directions, which give...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2025 |
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2025
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/214189 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Periodic -Systems and Nahm Sums: The Rank 2 Case. Yuma Mizuno. SIGMA 21 (2025), 094, 17 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | We classify periodic -systems of rank 2 satisfying the symplectic property. We find that there are six such -systems. In all cases, the periodicity follows from the existence of two reddening sequences associated with the time evolution of the -systems in positive and negative directions, which gives rise to quantum dilogarithm identities associated with Donaldson-Thomas invariants. We also consider q-series called the Nahm sums associated with these -systems. We see that they are included in Zagier's list of rank 2 Nahm sums that are likely to be modular functions. It was recently shown by Wang that they are indeed modular functions.
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| ISSN: | 1815-0659 |