Schubert problems, positivity and symbol letters

doi:10.1007/JHEP08(2022)168

CORC > 理论物理研究所 > 中国科学院理论物理研究所 > 理论物理所科研产出 > 理论物理所1978-2010年知识产出

	Schubert problems, positivity and symbol letters
	Yang, Qinglin 1
刊名	JOURNAL OF HIGH ENERGY PHYSICS
	2022
期号	8 页码:168
ISSN号	1029-8479
DOI	10.1007/JHEP08(2022)168
英文摘要	We propose a geometrical approach to generate symbol letters of amplitudes/integrals in planar N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N} $$\end{document} = 4 Super Yang-Mills theory, known as Schubert problems. Beginning with one-loop integrals, we find that intersections of lines in momentum twistor space are always ordered on a given line, once the external kinematics Z is in the positive region G(+)(4, n). Remarkably, cross-ratios of these ordered intersections on a line, which are guaranteed to be positive now, nicely coincide with symbol letters of corresponding Feynman integrals, whose positivity is then concluded directly from such geometrical configurations. In particular, we reproduce from this approach the 18 multiplicative independent algebraic letters for n = 8 amplitudes up to three loops. Finally, we generalize the discussion to two-loop Schubert problems and, again from ordered points on a line, generate a new kind of algebraic letters which mix two distinct square roots together. They have been found recently in the alphabet of two-loop double-box integral with n >= 9, and they are expected to appear in amplitudes at k + l >= 4.
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/311006/27851]
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.Chinese Acad Sci, Inst Theoret Phys, CAS Key Lab Theoret Phys, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Phys Sci, 19A Yuquan Rd, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Yang, Qinglin. Schubert problems, positivity and symbol letters[J]. JOURNAL OF HIGH ENERGY PHYSICS,2022(8):168.
APA	Yang, Qinglin.(2022).Schubert problems, positivity and symbol letters.JOURNAL OF HIGH ENERGY PHYSICS(8),168.
MLA	Yang, Qinglin."Schubert problems, positivity and symbol letters".JOURNAL OF HIGH ENERGY PHYSICS .8(2022):168.