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

Henriette Elvang, Yu-tin Huang, Cynthia Keeler, Thomas Lam, Timothy M. Olson, Samuel B. Roland, David E. Speyer
2014 Journal of High Energy Physics  
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
more » ... 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. Various properties of Grassmannian integrals are examined, including boundary properties, pole structure, and a homological interpretation of the global residue theorems for $\mathcal{N}=4$ SYM.
doi:10.1007/jhep12(2014)181 fatcat:td7atrpwczahnhdznjjtqazrgi