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The last few decades have seen many important advancements in our understanding of QFT scattering amplitudes, particularly in the case of $\mathcal{N}=4$ Super Yang-Mills (sYM). While $\mathcal{N}=4$ sYM is a useful playground where we can explore rich connections to geometry via constructions such as the positive Grassmanian, the amplituhedron, and on-shell diagrams, its less supersymmetric cousins must be understood from the same perspective as well if we are to generalize these modern methods to theories that are applicable to real life. One major piece of the puzzle is understanding the UV behavior of one of these structures, namely on-shell diagrams, for $\mathcal{N} < 4$, which is drastically different from $\mathcal{N}=4$ as the corresponding form now has UV poles. Furthermore, the $\mathcal{N} < 3$ behavior is even more strange, as it introduces higher order UV poles in the corresponding on-shell diagram form. This talk will focus on how to generalize the methods we developed for dealing with the UV behavior of planar $\mathcal{N}=3$ on-shell diagrams to the $\mathcal{N}<3$ case.

Pizza at 11:50am