MCTP-14-36 Grassmannians for scattering amplitudes in 4dN= 4SYM and 3d ABJM Henriette Elvang1, Yu-tin Huang2, Cynthia Keeler1, Thomas Lam3, Timothy M. Olson1, Samuel B. Roland1, David E Speyer3 1Michigan Center for Theoretical Physics & Randall Laboratory of Physics Department of Physics, University of Michigan, 450 Church St, Ann Arbor, MI 48109, USA 2Department of Physics and Astronomy, National Taiwan University, Taipei 10617, Taiwan, ROC 3Department of Mathematics, University of Michigan, 530 Church St, Ann Arbor, MI 48109, USA elvang, keelerc, tfylam, timolson, rolandsa, speyer@umich.edu, yutinyt@gmail.com Abstract Scattering amplitudes in 4dN= 4 super Yang-Mills theory (SYM) can be de- scribed by Grassmannian contour integrals whose form depends on whether the exter- nal 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 Grass- mannian integral for 3dN= 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. Various properties of Grassmannian integrals are examined, including boundary prop- erties, pole structure, and a homological interpretation of the global residue theorems forN= 4 SYM. arXiv:1410.0621v1 [hep-th] 2 Oct 2014
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