Geodesic
Combinatorics of the geometry of Wilson loop diagrams I: equivalence classes via matroids and polytopes
Canadian journal of mathematics, Tome 74 (2022) no. 4, pp. 1177-1208

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DOI

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) corresponds 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.
DOI : 10.4153/S0008414X21000134
Mots-clés : Wilson loop diagrams, NkMHV diagrams, positroids, N = 4 SYM theory 
Agarwala, Susama; Fryer, Siân; Yeats, Karen. Combinatorics of the geometry of Wilson loop diagrams I: equivalence classes via matroids and polytopes. Canadian journal of mathematics, Tome 74 (2022) no. 4, pp. 1177-1208. doi: 10.4153/S0008414X21000134
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     title = {Combinatorics of the geometry of {Wilson} loop diagrams {I:} equivalence classes via matroids and polytopes},
     journal = {Canadian journal of mathematics},
     pages = {1177--1208},
     year = {2022},
     volume = {74},
     number = {4},
     doi = {10.4153/S0008414X21000134},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X21000134/}
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