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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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2025 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2025
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| Онлайн доступ: | 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 |
| Цитувати: | Periodic -Systems and Nahm Sums: The Rank 2 Case. Yuma Mizuno. SIGMA 21 (2025), 094, 17 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862728271633842176 |
|---|---|
| author | Mizuno, Yuma |
| author_facet | Mizuno, Yuma |
| citation_txt | Periodic -Systems and Nahm Sums: The Rank 2 Case. Yuma Mizuno. SIGMA 21 (2025), 094, 17 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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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| first_indexed | 2026-03-21T18:00:50Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-214189 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T18:00:50Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Mizuno, Yuma 2026-02-20T07:58:52Z 2025 Periodic -Systems and Nahm Sums: The Rank 2 Case. Yuma Mizuno. SIGMA 21 (2025), 094, 17 pages 1815-0659 2020 Mathematics Subject Classification: 11F03; 11P84; 13F60 arXiv:2301.13239 https://nasplib.isofts.kiev.ua/handle/123456789/214189 https://doi.org/10.3842/SIGMA.2025.094 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. The authors would like to thank the anonymous referees for their constructive and helpful suggestions. This work is supported by JSPS KAKENHI Grant Number JP21J00050. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Periodic -Systems and Nahm Sums: The Rank 2 Case Article published earlier |
| spellingShingle | Periodic -Systems and Nahm Sums: The Rank 2 Case Mizuno, Yuma |
| title | Periodic -Systems and Nahm Sums: The Rank 2 Case |
| title_full | Periodic -Systems and Nahm Sums: The Rank 2 Case |
| title_fullStr | Periodic -Systems and Nahm Sums: The Rank 2 Case |
| title_full_unstemmed | Periodic -Systems and Nahm Sums: The Rank 2 Case |
| title_short | Periodic -Systems and Nahm Sums: The Rank 2 Case |
| title_sort | periodic -systems and nahm sums: the rank 2 case |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/214189 |
| work_keys_str_mv | AT mizunoyuma periodicsystemsandnahmsumstherank2case |