The Amplituhedron

We can calculate the probability of something happening in the Standard Model by doing the calculations of the probability of each of the Feynmann diagrams for each of the possible ways that a particle could have gotten from point A to point B, according to the rules of quantum mechanics.  But, it turns out that the number of possible ways that this could happen is infinite and that one has to do the calculations for a great many Feynmann diagrams simply to get a very close, but not exact, result.

Nina Arkani-Hamed, a leading string theorist, and Jaroslav Trnka, have discovered a way of doing the same calculations much more efficiently in a quantum mechanical toy model theory similar to the Standard Model called a maximally supersymmetric gauge theory in the Planar limit called Planar N=4 SYM, with the promise that many of their results will generalize to other quantum mechanical theories that lack some of the symmetries that make the calculations particularly easy, although not necessarily a generalization that could reach completely to the Standard Model.

In some situations, with the correctly chosen parameters, the toy model calculation results are very similar to those that would be produced in the Standard Model itself.

They do by constructing a polyhedron in a theoretical amplitude-space with certain properties that organize the many calculations that go into the conventional Feymann diagram approach such that the volume of the constructed polyhedron corresponds to the probability of a particle going from point A to point B according to the rules of quantum mechanics.  While this polyhedron is divorced from reality in its details, it turns out that this is done in a way that preserves locality and makes all the probabilities of every possible event add up to 100% even though it is not at all obvious from the method itself that this would work out to be the case.

At a minimum, it is a potential breakthrough in potential calculations.  It also arguably sheds light on underlying structure in amplitude calculations that had not previously been fully appreciated which may shed light on fundamental physics.

This is done from a supersymmetric/string theory perspective, but it may be that the assumptions can be fit to the more ideosyncratic case of the true Standard Model or to a SUSY theory that is effectively identical to the Standard Model at low energies.  A number of companion papers to flesh out the much hyped breakthrough have been promised.