Grassmannians for scattering amplitudes in 4d N=4 SYM and 3d ABJM

Henriette Elvang, Yu Tin Huang, Cynthia Keeler, Thomas Lam, Timothy M. Olson, Samuel B. Roland, David E. Speyer

Research output: Contribution to journalArticle

17 Scopus citations


Abstract: Scattering amplitudes in 4d 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 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. Various properties of Grassmannian integrals are examined, including boundary properties, pole structure, and a homological interpretation of the global residue theorems for N=4 SYM.

Original languageEnglish (US)
Article number181
JournalJournal of High Energy Physics
Issue number12
StatePublished - Jan 1 2014
Externally publishedYes


  • Differential and Algebraic Geometry
  • Scattering Amplitudes
  • Supersymmetric gauge theory

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

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    Elvang, H., Huang, Y. T., Keeler, C., Lam, T., Olson, T. M., Roland, S. B., & Speyer, D. E. (2014). Grassmannians for scattering amplitudes in 4d N=4 SYM and 3d ABJM. Journal of High Energy Physics, 2014(12), [181].