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

Abstract

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. 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.

arXiv comment52 pages, 5 figures

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Cited by in corpus (20)

• Evidence for a Nonplanar Amplituhedron
• On-shell Diagrams, Graßmannians and Integrability for Form Factors
• Gravity On-shell Diagrams
• The Amplituhedron and the One-loop Grassmannian Measure
• Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops
• The momentum amplituhedron of SYM and ABJM from twistor-string maps
• The orthogonal momentum amplituhedron and ABJM amplitudes
• All-Loop Four-Point Aharony-Bergman-Jafferis-Maldacena Amplitudes from Dimensional Reduction of the Amplituhedron
• Grassmannians and form factors with $q^2=0$ in N=4 SYM theory
• Wilson lines, Grassmannians and Gauge Invariant Off-shell Amplitudes in N=4 SYM
• On-shell diagrams and the geometry of planar N < 4 SYM theories
• Emergent unitarity, all-loop cuts and integrations from the ABJM amplituhedron
• The two-loop eight-point amplitude in ABJM theory
• On the geometry of the orthogonal momentum amplituhedron
• ABJM Amplitudes in U-gauge and a Soft Theorem
• Quantum noncommutative ABJM theory: first steps
• Top-forms of Leading Singularities in Nonplanar Multi-loop Amplitudes
• ABJM flux-tube and scattering amplitudes
• Positivity, Grassmannian Geometry and Simplex-like Structures of Scattering Amplitudes
• Simplex-like Structures of Maximally Supersymmetric Scattering Amplitudes