Combinatorics of the geometry of Wilson loop diagrams I: equivalence\n classes via matroids and polytopes

2019/08/28 by Susama Agarwala, Agarwala, Susama, Siân Fryer +3
Computer Science · Mathematics · #81T60 #Coding theory and cryptography #Combinatorics (math.CO) #Digital Image Processing Techniques #FOS: Mathematics #FOS: Physical sciences #Finite Group Theory Research #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.1908.10919

openalex publication_date 2019/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Wilson loop diagrams are an important tool in studying scattering amplitudes\nof SYM N=4 theory and are known by previous work to be associated to\npositroids. We characterize the conditions under which two Wilson loop diagrams\ngive the same positroid, prove that an important subclass of subdiagrams (exact\nsubdiagrams) correspond to uniform matroids, and enumerate the number of\ndifferent Wilson loop diagrams that correspond to each positroid cell. We also\ngive a correspondence between those positroids which can arise from Wilson loop\ndiagrams and directions in associahedra.\n

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