Geodesic
Combinatorics of the geometry of Wilson loop diagrams II: Grassmann necklaces, dimensions, and denominators
Canadian journal of mathematics, Tome 74 (2022) no. 6, pp. 1625-1672

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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. In this paper, we study the structure of the associated positroids, as well as the structure of the denominator of the integrand defined by each diagram. We give an algorithm to derive the Grassmann necklace of the associated positroid directly from the Wilson loop diagram, and a recursive proof that the dimension of these cells is thrice the number of propagators in the diagram. We also show that the ideal generated by the denominator in the integrand is the radical of the ideal generated by the product of Grassmann necklace minors.
DOI : 10.4153/S0008414X21000377
Mots-clés : Wilson loop diagrams, positroids, Grassmann necklace, Le diagram 
Agarwala, Susama; Fryer, Siân; Yeats, Karen. Combinatorics of the geometry of Wilson loop diagrams II: Grassmann necklaces, dimensions, and denominators. Canadian journal of mathematics, Tome 74 (2022) no. 6, pp. 1625-1672. doi: 10.4153/S0008414X21000377
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     title = {Combinatorics of the geometry of {Wilson} loop diagrams {II:} {Grassmann} necklaces, dimensions, and denominators},
     journal = {Canadian journal of mathematics},
     pages = {1625--1672},
     year = {2022},
     volume = {74},
     number = {6},
     doi = {10.4153/S0008414X21000377},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X21000377/}
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