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Combinatorics of the geometry of Wilson loop diagrams I: equivalence classes via matroids and polytopes
- Part of
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- Journal:
- Canadian Journal of Mathematics / Volume 74 / Issue 4 / August 2022
- Published online by Cambridge University Press:
- 26 February 2021, pp. 1177-1208
- Print publication:
- August 2022
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- Article
- Export citation
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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.
