Amplitudes and QFT

Scattering amplitudes are the arena where quantum field theory directly confronts experiment. At the LHC, quarks and gluons inside each proton slam together under the influence of quantum chromodynamics (QCD), producing a cornucopia of jets, electroweak bosons, the occasional Higgs boson, and perhaps the needles of new physics inside the haystack of the Standard Model. Advances in our theoretical understanding of scattering amplitudes have a practical benefit: they enable more precise predictions of Standard Model cross sections at the LHC, which in turn assist experimental measurements and searches for new particles. Yet these advances have also revealed beautiful and intriguing structures and patterns, both within individual theories and relating different theories to each other, which suggest that our fundamental understanding of quantum field theory is far from complete.

A toy model for QCD is its supersymmetric cousin, N=4 super-Yang-Mills theory.  In the limit that the number of colors is very large, this theory has remarkable properties, including quantum integrability, a duality between amplitudes and polygonal Wilson loops, and a "maximal transcendentality" relationship to QCD. Lance Dixon's group has been exploring amplitudes in this theory to high loop order by "bootstrapping": writing down an ansatz for the amplitude in a space of functions, and then imposing constraints to determine it uniquely. This approach has succeeded for six gluon amplitudes to 7 loop orders in perturbation theory, and an amplitude for a "Higgs boson" and three gluons to 8 loops.  These results are for functions of multiple variables; they go far beyond what can be done in other theories, and provide important insight into perturbative gauge theory and the connection to strong coupling, as well as revealing intricate mathematical structure.  In fact, they have revealed a strange “antipodal” duality between the above processes through 7 loops; this duality exchanges branch cuts and derivatives, and extends to other processes too, but it’s physical origin remains to be understood.

There is also much interest in applying similar ideas to QCD observables; one avenue has been the energy-energy-correlator, both its general analytic behavior and resummation of its small-angle limit have been explored.