Notes on Worldsheet-Like Variables for Cluster Configuration Spaces
We continue the exploration of various appearances of cluster algebras in scattering amplitudes and related topics in physics. The cluster configuration spaces generalize the familiar moduli space ℳ₀‚ₙ to finite-type cluster algebras. We study worldsheet-like variables, which for classical types hav...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2023 |
| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2023
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211986 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Notes on Worldsheet-Like Variables for Cluster Configuration Spaces. Song He, Yihong Wang, Yong Zhang and Peng Zhao. SIGMA 19 (2023), 045, 24 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862671053221789696 |
|---|---|
| author | He, Song Wang, Yihong Zhang, Yong Zhao, Peng |
| author_facet | He, Song Wang, Yihong Zhang, Yong Zhao, Peng |
| citation_txt | Notes on Worldsheet-Like Variables for Cluster Configuration Spaces. Song He, Yihong Wang, Yong Zhang and Peng Zhao. SIGMA 19 (2023), 045, 24 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We continue the exploration of various appearances of cluster algebras in scattering amplitudes and related topics in physics. The cluster configuration spaces generalize the familiar moduli space ℳ₀‚ₙ to finite-type cluster algebras. We study worldsheet-like variables, which for classical types have also appeared in the study of the symbol alphabet of Feynman integrals. We provide a systematic derivation of these variables from -systems, which allows us to express the dihedral coordinates in terms of them and to write the corresponding cluster string integrals in compact forms. We mainly focus on the ₙ type and show how to reach the boundaries of the configuration space, and write the saddle-point equations in terms of these variables. Moreover, these variables make it easier to study various topological properties of the space using a finite-field method. We propose conjectures about quasi-polynomial point count, dimensions of cohomology, and the number of saddle points for the ₙ space up to = 10, which greatly extend earlier results.
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| first_indexed | 2026-03-16T14:45:56Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211986 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-16T14:45:56Z |
| publishDate | 2023 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | He, Song Wang, Yihong Zhang, Yong Zhao, Peng 2026-01-20T16:14:35Z 2023 Notes on Worldsheet-Like Variables for Cluster Configuration Spaces. Song He, Yihong Wang, Yong Zhang and Peng Zhao. SIGMA 19 (2023), 045, 24 pages 1815-0659 2020 Mathematics Subject Classification: 13F60; 05E14; 81T30 arXiv:2109.13900 https://nasplib.isofts.kiev.ua/handle/123456789/211986 https://doi.org/10.3842/SIGMA.2023.045 We continue the exploration of various appearances of cluster algebras in scattering amplitudes and related topics in physics. The cluster configuration spaces generalize the familiar moduli space ℳ₀‚ₙ to finite-type cluster algebras. We study worldsheet-like variables, which for classical types have also appeared in the study of the symbol alphabet of Feynman integrals. We provide a systematic derivation of these variables from -systems, which allows us to express the dihedral coordinates in terms of them and to write the corresponding cluster string integrals in compact forms. We mainly focus on the ₙ type and show how to reach the boundaries of the configuration space, and write the saddle-point equations in terms of these variables. Moreover, these variables make it easier to study various topological properties of the space using a finite-field method. We propose conjectures about quasi-polynomial point count, dimensions of cohomology, and the number of saddle points for the ₙ space up to = 10, which greatly extend earlier results. We thank Zhenjie Li, Qinglin Yang, and Yichao Tang for collaborations on related projects, and Yang Zhang for help with the USTC computing platform. YZ would like to thank Alex Edison for the discussions on the number of independent forms. PZ would like to thank Yuqi Li for the discussions on the string worldsheet. We thank the anonymous referees for detailed comments that help improve the presentation of the draft. SH’s research was supported in part by the National Natural Science Foundation of China under Grant Nos. 11935013, 11947301, 12047502, 12047503, 12247103, 12225510. The research of YZ is supported by the Knut and Alice Wallenberg Foundation under the grant KAW 2018.0116: From Scattering Amplitudes to Gravitational Waves. PZ is supported by a China Postdoctoral Science Foundation Special Fund, grant number Y9Y2231. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Notes on Worldsheet-Like Variables for Cluster Configuration Spaces Article published earlier |
| spellingShingle | Notes on Worldsheet-Like Variables for Cluster Configuration Spaces He, Song Wang, Yihong Zhang, Yong Zhao, Peng |
| title | Notes on Worldsheet-Like Variables for Cluster Configuration Spaces |
| title_full | Notes on Worldsheet-Like Variables for Cluster Configuration Spaces |
| title_fullStr | Notes on Worldsheet-Like Variables for Cluster Configuration Spaces |
| title_full_unstemmed | Notes on Worldsheet-Like Variables for Cluster Configuration Spaces |
| title_short | Notes on Worldsheet-Like Variables for Cluster Configuration Spaces |
| title_sort | notes on worldsheet-like variables for cluster configuration spaces |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211986 |
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