Scattering forms and the positive geometry of kinematics, color and the worldsheet

doi:10.1007/JHEP05(2018)096

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	Scattering forms and the positive geometry of kinematics, color and the worldsheet
	Yan, GW ; Arkani-Hamed, N ; Bai, YT ; He, S 1,2
刊名	JOURNAL OF HIGH ENERGY PHYSICS
	2018
期号	5 页码:96
关键词	GAUGE-THEORY AMPLITUDES TREE
ISSN号	1029-8479
DOI	10.1007/JHEP05(2018)096
英文摘要	The search for a theory of the S-Matrix over the past five decades has revealed surprising geometric structures underlying scattering amplitudes ranging from the string worldsheet to the amplituhedron, but these are all geometries in auxiliary spaces as opposed to the kinematical space where amplitudes actually live. Motivated by recent advances providing a reformulation of the amplituhedron and planar N = 4 SYM amplitudes directly in kinematic space, we propose a novel geometric understanding of amplitudes in more general theories. The key idea is to think of amplitudes not as functions, but rather as differential forms on kinematic space. We explore the resulting picture for a wide range of massless theories in general spacetime dimensions. For the bi-adjoint phi(3) scalar theory, we establish a direct connection between its "scattering form" and a classic polytope the associahedron - known to mathematicians since the 1960's. We find an associahedron living naturally in kinematic space, and the tree level amplitude is simply the "canonical form" associated with this "positive geometry". Fundamental physical properties such as locality and unitarity, as well as novel "soft" limits, are fully determined by the combinatorial geometry of this polytope. Furthermore, the moduli space for the open string worldsheet has also long been recognized as an associahedron. We show that the scattering equations act as a diffeomorphism between the interior of this old "worldsheet associahedron" and the new "kinematic associahedron", providing a geometric interpretation and simple conceptual derivation of the bi-adjoint CHY formula. We also find "scattering forms" on kinematic space for Yang-Mills theory and the Non-linear Sigma Model, which are dual to the fully color-dressed amplitudes despite having no explicit color factors. This is possible due to a remarkable fact "Color is Kinematics" whereby kinematic wedge products in the scattering forms satisfy the same Jacobi relations as color factors. Finally, all our scattering forms are well-defined on the projectivized kinematic space, a property which can be seen to provide a geometric origin for color-kinematics duality.
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/311006/22900]
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.Princeton Univ, Dept Phys, Princeton, NJ 08544 USA 2.Chinese Acad Sci, Inst Theoret Phys, CAS Key Lab Theoret Phys, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, 19A Yuquan Rd, Beijing 100049, Peoples R China 4.Tsinghua Univ, Inst Adv Study, Beijing 100084, Peoples R China 5.Inst Adv Study, Sch Nat Sci, Olden Lane, Princeton, NJ 08540 USA
推荐引用方式 GB/T 7714	Yan, GW,Arkani-Hamed, N,Bai, YT,et al. Scattering forms and the positive geometry of kinematics, color and the worldsheet[J]. JOURNAL OF HIGH ENERGY PHYSICS,2018(5):96.
APA	Yan, GW,Arkani-Hamed, N,Bai, YT,&He, S.(2018).Scattering forms and the positive geometry of kinematics, color and the worldsheet.JOURNAL OF HIGH ENERGY PHYSICS(5),96.
MLA	Yan, GW,et al."Scattering forms and the positive geometry of kinematics, color and the worldsheet".JOURNAL OF HIGH ENERGY PHYSICS .5(2018):96.