Truncated cluster algebras and Feynman integrals with algebraic letters

doi:10.1007/JHEP12(2021)110

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	Truncated cluster algebras and Feynman integrals with algebraic letters
	He, Song 1,2,3,4; Li, Zhenjie 1; Yang, Qinglin 1
刊名	JOURNAL OF HIGH ENERGY PHYSICS
	2021
期号	12 页码:110
ISSN号	1029-8479
DOI	10.1007/JHEP12(2021)110
英文摘要	We propose that the symbol alphabet for classes of planar, dual-conformalinvariant Feynman integrals can be obtained as truncated cluster algebras purely from their kinematics, which correspond to boundaries of (compactifications of) G + (4, n)/T for the n-particle massless kinematics. For one-, two-, three-mass-easy hexagon kinematics with n = 7, 8, 9, we find finite cluster algebras D-4, D-5 and D-6 respectively, in accordance with previous result on alphabets of these integrals. As the main example, we consider hexagon kinematics with two massive corners on opposite sides and find a truncated affine D-4 cluster algebra whose polytopal realization is a co-dimension 4 boundary of that of G + (4, 8)/T with 39 facets; the normal vectors for 38 of them correspond to g-vectors and the remaining one gives a limit ray, which yields an alphabet of 38 rational letters and 5 algebraic ones with the unique four-mass-box square root. We construct the space of integrable symbols with this alphabet and physical first-entry conditions, whose dimension can be reduced using conditions from a truncated version of cluster adjacency. Already at weight 4, by imposing last-entry conditions inspired by the n = 8 double-pentagon integral, we are able to uniquely determine an integrable symbol that gives the algebraic part of the most generic double-pentagon integral. Finally, we locate in the space the n = 8 double-pentagon ladder integrals up to four loops using differential equations derived from Wilson-loop d log forms, and we find a remarkable pattern about the appearance of algebraic letters.
学科主题	Physics
语种	英语
内容类型	期刊论文
源URL	[http://ir.itp.ac.cn/handle/311006/27678]
专题	理论物理研究所_理论物理所1978-2010年知识产出
作者单位	1.Int Ctr Theoret Phys Asia Pact, ICTP AP, Beijing, Peoples R China 2.Univ Chinese Acad Sci, Sch Phys Sci, 19A Yuquan Rd, Beijing 100049, Peoples R China 3.Chinese Acad Sci, Inst Theoret Phys, CAS Key Lab Theoret Phys, Beijing 100190, Peoples R China 4.UCAS, Hangzhou Inst Adv Study, Sch Fundamental Phys & Math Sci, Hangzhou 310024, Peoples R China 5.Peng Huanwu Ctr Fundamental Theory, Hefei 230026, Anhui, Peoples R China
推荐引用方式 GB/T 7714	He, Song,Li, Zhenjie,Yang, Qinglin. Truncated cluster algebras and Feynman integrals with algebraic letters[J]. JOURNAL OF HIGH ENERGY PHYSICS,2021(12):110.
APA	He, Song,Li, Zhenjie,&Yang, Qinglin.(2021).Truncated cluster algebras and Feynman integrals with algebraic letters.JOURNAL OF HIGH ENERGY PHYSICS(12),110.
MLA	He, Song,et al."Truncated cluster algebras and Feynman integrals with algebraic letters".JOURNAL OF HIGH ENERGY PHYSICS .12(2021):110.