Finally The Amplituhedron Paper

[MTd2]

http://arxiv.org/abs/1312.2007

The Amplituhedron

Nima Arkani-Hamed, Jaroslav Trnka
(Submitted on 6 Dec 2013)
Perturbative scattering amplitudes in gauge theories have remarkable simplicity and hidden infinite dimensional symmetries that are completely obscured in the conventional formulation of field theory using Feynman diagrams. This suggests the existence of a new understanding for scattering amplitudes where locality and unitarity do not play a central role but are derived consequences from a different starting point. In this note we provide such an understanding for N=4 SYM scattering amplitudes in the planar limit, which we identify as ``the volume" of a new mathematical object--the Amplituhedron--generalizing the positive Grassmannian. Locality and unitarity emerge hand-in-hand from positive geometry.

 

[Haelfix]

This is a beautiful, important, albeit late paper (eg most of the main insights have been known for months now). One that really has a lot of different great physicists stamp on it. It's hard not to notice Maldecena, Witten and Cachazo's distinctive and idiosyncratic insights in the structure of the insights.

I happen to believe the previous generalization in this program was arguably more important (the positive Grassmanian papers) but this is nevertheless a clear step forward. I also happen to believe there is yet another fundamental generalization that remains to be discovered and that underlies the move from from the planar limit (and one that generalizes to arbitrary renormalizations).

In terms of research directions, there should be a legion of graduate students working on specific examples.

 

[Paul Colby]

Okay, let us assume this is a fantastic new discovery. Is it fair to ask "where is the beef?" If this is a great new way to compute amplitudes then is the technique being applied to say QED computations, QCD phenomenology? If it is being applied, does it get the right answers?

 

[Haelfix]

Yes. These techniques and their precursors were originally used several years ago to compute amplitudes for QCD background estimation at the LHC. They drastically simplify the amount of algebraic work necessary to calculate certain diagrams (with large amounts of incoming particles). So yes, the answers are correct.