Grassmannians for scattering amplitudes in 4d $\mathcal{N}=4$ SYM and 3d ABJM

Understand

Scattering amplitudes in 4d $\mathcal{N}=4$ super Yang-Mills theory (SYM) can be described by Grassmannian contour integrals whose form depends on whether the external data is encoded in momentum space, twistor space, or momentum twistor space.

• After a pedagogical review, we present a new, streamlined proof of the equivalence of the three integral formulations.
• A similar strategy allows us to derive a new Grassmannian integral for 3d $\mathcal{N}=6$ ABJM theory amplitudes in momentum twistor space: it is a contour integral in an orthogonal Grassmannian with the novel property that the internal metric depends on the external data.
• The result can be viewed as a central step towards developing an amplituhedron formulation for ABJM amplitudes.