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This is way over my head, both mathematically and in terms of what that math is describing, specifically the 'superpartner particles'.
I haven't even heard of the technique that makes Feynman diagrams seem like the long way to do it.
This description sounds promising, but string theory has sounded promising for decades, with no tangible verifiable predictions. As such, I think a healthy dose of skepticism is in order while the data, if any, comes in.
It also sounds like they've started from some rather confining assumptions (which is common), and the theory needs to be developed to see how robust it is in a broader context (also quite common).
What can they mean here?
"But the new amplituhedron research suggests space-time, and therefore dimensions, may be illusory anyway."
That does not sound like physics... or mathematics for that matter. It sounds like Savy told them to say that, just to troll me. 
(much respect, Savy )
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