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I am reading the book by Arkani-Hamed et al. I see how one can get the permutation from a plabic graph, and I see how different plabic graphs can be shown to be equivalent through moves. But I don't see how to start from the scattering information (how many particles scatter, and how many have negative helicities, and maybe the Feynman diagram loop order, although I know this last parameter is not central in plabic graphs) to the corresponding plabic graphs. What is the algorithm? (by the way, I do know how to get from a permutation to a graph, using BCFW bridges as on page 68 of the book).

Thanks to anyone who can help.

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    $\begingroup$ Consider to be more explicit as a gesture to readers who doesn't have the book. $\endgroup$
    – Qmechanic
    Commented May 25, 2021 at 13:13
  • $\begingroup$ Thanks for the comment. This is a vey technical topic. It's clear that only people who are already quite knowledgeable of the topic can help answer the question. People who are not familiar with the topic won't be able to answer the question. For example, if someone has a question about N=8 SUGRA, the person won't be expected to teach what SUGRA is and what supersymmetry is. But that you for your comment. $\endgroup$
    – Patrick
    Commented May 25, 2021 at 21:19

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The number of particles is equal to the number of external legs in the plabic graph. The number of negative helicity particles is usually indicated by k and can be read from the permutation labelling the plabic graph.

The BCFW recursion tells you what set of plabic graph you have to sum to get the amplitude.

Alternatively, the amplituhedron gives you a nice answer to what set of plabic graph you have to sum. To each plabic graph you can associate a region in the space where the amplituhedron is defined. The sum of a set of plabic graph whose image tesselate the $A_{n,k}$ amplituhedron gives you the correspondent $\mathcal{A}_{n,k}$ super amplitude.

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