ABJM amplitudes and the positive orthogonal grassmannian

Abstract

A remarkable connection between perturbative scattering amplitudes of four-dimensional planar SYM, and the stratification of the positive grassmannian, was revealed in the seminal work of Arkani-Hamed et. al. Similar extension for three-dimensional ABJM theory was proposed. Here we establish a direct connection between planar scattering amplitudes of ABJM theory, and singularities there of, to the stratification of the positive orthogonal grassmannian. In particular, scattering processes are constructed through on-shell diagrams, which are simply iterative gluing of the fundamental four-point amplitude. Each diagram is then equivalent to the merging of fundamental OG_2 orthogonal grassmannian to form a larger OG_k, where 2k is the number of external particles. The invariant information that is encoded in each diagram is precisely this stratification. This information can be easily read off via permutation paths of the on-shell diagram, which also can be used to derive a canonical representation of OG_k that manifests the vanishing of consecutive minors as the singularity of all on-shell diagrams. Quite remarkably, for the BCFW recursion representation of the tree-level amplitudes, the on-shell diagram manifests the presence of all physical factorization poles, as well as the cancellation of the spurious poles. After analytically continuing the orthogonal grassmannian to split signature, we reveal that each on-shell diagram in fact resides in the positive cell of the orthogonal grassmannian, where all minors are positive. In this language, the amplitudes of ABJM theory is simply an integral of a product of dlog forms, over the positive orthogonal grassmannian.

52 pages: v2, typos corrected, published version in JHEP

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Cited by in corpus (41)

• The Amplituhedron
• Unwinding the Amplituhedron in Binary
• Evidence for a Nonplanar Amplituhedron
• Prescriptive Unitarity
• On-shell Diagrams, Graßmannians and Integrability for Form Factors
• Gravity On-shell Diagrams
• Stratifying On-Shell Cluster Varieties: the Geometry of Non-Planar On-Shell Diagrams
• Notes on Scattering Amplitudes as Differential Forms
• Grassmannians for scattering amplitudes in 4d $\mathcal{N}=4$ SYM and 3d ABJM
• Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops
• Integrable Amplitude Deformations for N=4 Super Yang-Mills and ABJM Theory
• The orthogonal momentum amplituhedron and ABJM amplitudes
• Ising model and the positive orthogonal Grassmannian
• The momentum amplituhedron of SYM and ABJM from twistor-string maps
• On the ABJM four-point amplitude at three loops and BDS exponentiation
• All-Loop Four-Point Aharony-Bergman-Jafferis-Maldacena Amplitudes from Dimensional Reduction of the Amplituhedron
• The Geometry of On-Shell Diagrams
• Non-planarity through unitarity in ABJM
• On-shell diagrams and the geometry of planar N < 4 SYM theories
• Unified Formalism for 6D Superamplitudes Based on a Symplectic Grassmannian
• Integrated negative geometries in ABJM
• Positroid Stratification of Orthogonal Grassmannian and ABJM Amplitudes
• On-shell diagrammatics and the perturbative structure of planar gauge theories
• The Loop Momentum Amplituhedron
• Dual Superconformal Symmetry of $\mathcal{N}=2$ Chern-Simons theory with Fundamental Matter at Large $N$
• Cluster Algebras and the Positive Grassmannian
• 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
• Non-Planar On-Shell Diagrams
• Anatomy of the Amplituhedron
• Logarithmic Singularities and Maximally Supersymmetric Amplitudes
• The Positive orthogonal Grassmannian and loop amplitudes of ABJM
• Dualities for Ising networks
• ABJM flux-tube and scattering amplitudes
• Bonus scaling and BCFW in N=7 supergravity
• Orientations of BCFW Charts on the Grassmannian
• Symplectic Grassmannians, dual conformal symmetry and 4-point amplitudes in 6D
• The Aharony-Bergman-Jafferis-Maldacena theory on a circle
• The Geometry of BCFW for ABJM Loop Integrands
• The uncrossing partial order on matchings is Eulerian