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Symmetry, Integrability and Geometry: Methods and Applications, 2023, Volume 19, 045, 24 pp.
DOI: https://doi.org/10.3842/SIGMA.2023.045
(Mi sigma1940)
 

This article is cited in 3 scientific papers (total in 3 papers)

Notes on Worldsheet-Like Variables for Cluster Configuration Spaces

Song Heabcde, Yihong Wangdacf, Yong Zhanggh, Peng Zhaoa

a CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, 100190 Beijing, P.R. China
b International Centre for Theoretical Physics Asia-Pacific, Beijing/Hangzhou, P.R. China
c School of Physical Sciences, University of Chinese Academy of Sciences, No. 19A Yuquan Road, 100049 Beijing, P.R. China
d School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS, 310024 Hangzhou, P.R. China
e Peng Huanwu Center for Fundamental Theory, Hefei, 230026 Anhui, P.R. China
f Laboratoire d'Annecy-le-Vieux de Physique Théorique, Université Savoie Mont Blanc, 9 Chemin de Bellevue, 74941 Annecy-le-Vieux, France
g Perimeter Institute, 31 Caroline Street North, Waterloo, Ontario, N2L 2Y5, Canada
h Department of Physics and Astronomy, Uppsala University, 75108 Uppsala, Sweden
Full-text PDF (605 kB) Citations (3)
References:
Abstract: 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 ${\mathcal M}_{0,n}$ 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 $Y$-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 $D_n$ 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 $D_n$ space up to $n=10$, which greatly extend earlier results.
Keywords: cluster algebras, generalized associahedra, $Y$-systems, string amplitudes.
Funding agency Grant number
National Natural Science Foundation of China 11935013
11947301
12047502
12047503
12247103
12225510
Knut and Alice Wallenbergs Foundation KAW 2018.0116
China Postdoctoral Science Foundation Y9Y2231
SH's research was supported in part by the National Natural Science Foundation of China under Grant No. 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.
Received: November 21, 2022; in final form June 29, 2023; Published online July 12, 2023
Document Type: Article
MSC: 13F60, 05E14, 81T30
Language: English
Citation: Song He, Yihong Wang, Yong Zhang, Peng Zhao, “Notes on Worldsheet-Like Variables for Cluster Configuration Spaces”, SIGMA, 19 (2023), 045, 24 pp.
Citation in format AMSBIB
\Bibitem{HeWanZha23}
\by Song~He, Yihong~Wang, Yong~Zhang, Peng~Zhao
\paper Notes on Worldsheet-Like Variables for Cluster Configuration Spaces
\jour SIGMA
\yr 2023
\vol 19
\papernumber 045
\totalpages 24
\mathnet{http://mi.mathnet.ru/sigma1940}
\crossref{https://doi.org/10.3842/SIGMA.2023.045}
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    Citing articles in Google Scholar: Russian citations, English citations
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    Symmetry, Integrability and Geometry: Methods and Applications
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