In discussing the amplithedron I made a point of mentioning that it's virtue (for the theory for which it works) is that it removes the gauge redundancy. Peter Woit has (quite rightly) chastised me for calling the gauge degrees of freedom a nuisance. Now of course they are much more than that. All the quantum field theories that work in the real world have local gauge symmetries, and those symmetries are essential for conservation laws, renormalizability and lots of stuff that smarter people than I understand.
The fact is, though, that they have a lot of redundancy in the sense that we have infinitely many physically equivalent descriptions of the same phenomena. That turns out to pose computational problems. Why, we might ask, would God make a universe like that? Arkani-Hamed and the amplituhedron authors conjecture that the redundancy is a consequence of a faulty fundamental description based on locality and unitarity. For one very special and non-physical QFT they seem to have shown that that is the case. If the notion is more widely applicable, it could be revolutionary.