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2021

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


Abstract

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


Citation

@onlineAgarwala_2019 author: Agarwala Susama and Fryer Siân and Yeats Karen title: Combinatorics of the geometry of Wilson loop diagrams I: equivalence classes via matroids and polytopes year: 2019 month: Aug eprinttype

Citation

@onlineAgarwala_2019 author: Agarwala Susama and Fryer Siân and Yeats Karen title: Combinatorics of the geometry of Wilson loop diagrams I: equivalence classes via matroids and polytopes year: 2019 month: Aug eprinttype