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Notes on Worldsheet : Like Variables for Cluster Configuration Spaces
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- He, Song (author)
- UCAS, Hangzhou Inst Adv Study, Sch Fundamental Phys & Math Sci, Hangzhou 310024, Peoples R China.;Chinese Acad Sci, Inst Theoret Phys, CAS Key Lab Theoret Phys, Beijing 100190, Peoples R China.;Int Ctr Theoret Phys Asia Pacific, Beijing, Peoples R China.;Univ Chinese Acad Sci, Sch Phys Sci, 19A Yuquan Rd, Beijing 100049, Peoples R China.;Peng Huanwu Ctr Fundamental Theory, Hefei 230026, Anhui, Peoples R China.
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- Wang, Yihong (author)
- UCAS, Hangzhou Inst Adv Study, Sch Fundamental Phys & Math Sci, Hangzhou 310024, Peoples R China.;Chinese Acad Sci, Inst Theoret Phys, CAS Key Lab Theoret Phys, Beijing 100190, Peoples R China.;Univ Chinese Acad Sci, Sch Phys Sci, 19A Yuquan Rd, Beijing 100049, Peoples R China.;Univ Savoie Mont Blanc, Lab Annecy Le Vieux Phys Theor, 9 Chemin Bellevue, F-74941 Annecy Le Vieux, France.
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- Zhang, Yong (author)
- Uppsala universitet,Teoretisk fysik,Perimeter Inst, 31 Caroline St North, Waterloo, ON N2L 2Y5, Canada.
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- UCAS, Hangzhou Inst Adv Study, Sch Fundamental Phys & Math Sci, Hangzhou 310024, Peoples R China;Chinese Acad Sci, Inst Theoret Phys, CAS Key Lab Theoret Phys, Beijing 100190, Peoples R China.;Int Ctr Theoret Phys Asia Pacific, Beijing, Peoples R China.;Univ Chinese Acad Sci, Sch Phys Sci, 19A Yuquan Rd, Beijing 100049, Peoples R China.;Peng Huanwu Ctr Fundamental Theory, Hefei 230026, Anhui, Peoples R China. UCAS, Hangzhou Inst Adv Study, Sch Fundamental Phys & Math Sci, Hangzhou 310024, Peoples R China.;Chinese Acad Sci, Inst Theoret Phys, CAS Key Lab Theoret Phys, Beijing 100190, Peoples R China.;Univ Chinese Acad Sci, Sch Phys Sci, 19A Yuquan Rd, Beijing 100049, Peoples R China.;Univ Savoie Mont Blanc, Lab Annecy Le Vieux Phys Theor, 9 Chemin Bellevue, F-74941 Annecy Le Vieux, France. (creator_code:org_t)
- SIGMA (Symmetry, Integrability and Geometry: Methods and Application), 2023
- 2023
- English.
- In: Symmetry, Integrability and Geometry. - : SIGMA (Symmetry, Integrability and Geometry: Methods and Application). - 1815-0659. ; 19, s. 1-24
- Journal article (peer-reviewed)
Abstract
Subject headings
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- 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 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 Dn 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 Dn space up to n = 10, which greatly extend earlier results.
Subject headings
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
Keyword
- cluster algebras
- generalized associahedra
- Y-systems
- string amplitudes
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- ref (subject category)
- art (subject category)
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