Bern, Dixon and Kosower started working on amplitudes more than twenty years ago, at a time that it was becoming clear that string theory was not working out as a theory of everything. Calculations in string theory did though lead to interesting new ideas about how to evaluate scattering amplitudes in gauge theory (I see from Dixon’s list of publications that in 1994 he wrote something for the SLAC Beam Line on “Whatever happened to the theory of everything?”, presumably about this, but now too deep in the past to be available on-line).
The three Sakurai Prize winners have been steadily working at the problems of amplitudes in gauge theory and quantum gravity, for many years without getting much attention for their work. About ten years ago, things changed when Witten wrote a paper about getting amplitudes from the “twistor string”, a topological string theory in twistor space (the use of twistor space was originated by Penrose back in the late 1960s, and was applied by V.P. Nair to gauge theory amplitudes back in 1988 while he was here at Columbia).
About six years ago Nima Arkani-Hamed entered the subject, where he has had a dramatic effect as an impresario, arguing that this is a route to revolutionary ideas about physics, overthrowing conventional notions of space and time, locality and unitarity, and doing away with the notion that gauge invariance is important. This was partly responsible for his $3 million Milner prize.
https://www.math.columbia.edu/~woit/wordpress/?p=6476
For the latest along these lines, a paper with Trnka about “The Amplituhedron” has just appeared, a topic which got wide play in the press earlier this year as Physicists Discover Geometry Underlying Particle Physics, drawing a parody from Scott Aaronson about his own work on the “Unitarihedron” and “Diaperhedron”. Arkani-Hamed’s talk at the Symposium covers both the ideas of Bern, Dixon and Kosower and his recent work with Trnka.
More at link.
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