Wilson Loop Diagrams and Positroids

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• 作者：Susama Agarwala ; Eloi Marin-Amat
• 刊名：Communications in Mathematical Physics
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：350
• 期：2
• 页码：569-601
• 全文大小：911KB
• 刊物类别：Physics and Astronomy
• 刊物主题：Theoretical, Mathematical and Computational Physics; Mathematical Physics; Quantum Physics; Complex Systems; Classical and Quantum Gravitation, Relativity Theory;
• 出版者：Springer Berlin Heidelberg
• ISSN：1432-0916
• 卷排序：350

文摘

In this paper, we study a new application of the positive Grassmannian to Wilson loop diagrams (or MHV diagrams) for scattering amplitudes in N= 4 Super Yang–Mill theory (N = 4 SYM). There has been much interest in studying this theory via the positive Grassmannians using BCFW recursion. This is the first attempt to study MHV diagrams for planar Wilson loop calculations (or planar amplitudes) in terms of positive Grassmannians. We codify Wilson loop diagrams completely in terms of matroids. This allows us to apply the combinatorial tools in matroid theory used to identify positroids (non-negative Grassmannians) to Wilson loop diagrams. In doing so, we find that certain non-planar Wilson loop diagrams define positive Grassmannians. While non-planar diagrams do not have physical meaning, this finding suggests that they may have value as an algebraic tool, and deserve further investigation.