تقرير
Truncated cluster algebras and Feynman integrals with algebraic letters
العنوان: | Truncated cluster algebras and Feynman integrals with algebraic letters |
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المؤلفون: | He, Song, Li, Zhenjie, Yang, Qinglin |
سنة النشر: | 2021 |
المجموعة: | High Energy Physics - Theory |
مصطلحات موضوعية: | High Energy Physics - Theory |
الوصف: | We propose that the symbol alphabet for classes of planar, dual-conformal-invariant 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. Comment: v2: typos corrected and a comment on smaller alphabet added |
نوع الوثيقة: | Working Paper |
DOI: | 10.1007/JHEP12(2021)110 |
URL الوصول: | http://arxiv.org/abs/2106.09314 |
رقم الأكسشن: | edsarx.2106.09314 |
قاعدة البيانات: | arXiv |
DOI: | 10.1007/JHEP12(2021)110 |
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