Firenze and amplitudes

by landonlehman

I am headed to Firenze (Florence), Italy this weekend to attend a 3-week-long winter school at the Galileo Galilei Institute for Theoretical Physics. It should be a good place to meet some new people and perhaps come up with new ideas to explore. Perhaps there will be time to explore the city as well!

In December I thought about calculating Yang-Mills amplitudes in 6 dimensions by using the formalism outlined in a paper by Cheung and O’Connell. In the paper, they calculate the the 4- and 5-point amplitudes by using BCFW recursion on the 3-point amplitude. The interesting thing about 6-dimensional amplitudes is that all of the 4-dimensional helicity structures can be obtained from a single expression in 6 dimensions. For example, 4D MHV amplitudes are contained in the “general” 6D expression. So if there were a simple expression for an n-point 6D amplitude, like there is a simple expression for a 4D MHV n-point amplitude, it would contain all of the 4D tree-level amplitudes.

Unfortunately the 6D amplitudes become complicated very quickly. The 3-point amplitude must be written using special kinematic variables, and using these the 4-point amplitude can be deduced from BCFW. The 4-point Einstein gravity amplitude can also be obtained by using the KLT relations. The 4-point amplitude has a relatively simple structure, but applying BCFW to this structure and calculating the 5-point amplitude gives a very complicated expression (at least I think it is complicated!). Perhaps some new notation is needed in order to see the underlying structure. Or maybe 6D is just inherently more complicated than 4D, and it would be easy to just directly attack the 4D problem instead of solving it in 6D and reducing to 4D.

I also thought about the application of on-shell methods to effective field theories. This possibility has been explored for the nonlinear sigma model using “semi-on-shell” amplitudes. In general, adding masses to the spinor-helicity formalism makes it more complicated, and I am not sure what it means to integrate out a particle in this formalism. And since integrating out heavy particles from a Lagrangian is the most common form of generating an effective field theory, it would be useful to have a way to translate this procedure into spinor helicity language.

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