All-Loop Four-Point Aharony-Bergman-Jafferis-Maldacena Amplitudes from Dimensional Reduction of the Amplituhedron

Abstract

We define a new geometry obtained from the all-loop amplituhedron in $\mathcal{N}=4$ SYM by reducing its four-dimensional external and loop momenta to three dimensions. Focusing on the simplest four-point case, we provide strong evidence that the canonical form of this ``reduced amplituhedron" gives the all-loop integrand of the ABJM four-point amplitude. In addition to various all-loop cuts manifested by the geometry, we present explicitly new results for the integrand up to five loops, which are much simpler than results in $\mathcal{N}=4$ SYM. One of the reasons for such all-loop simplifications is that only a very small fraction of the so-called negative geometries survive the dimensional reduction, which corresponds to bipartite graphs. Our results suggest an unexpected relation between four-point amplitudes in these two theories.

arXiv comment5 pages + appendices, version accepted in PRL

References in corpus (40)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• The Amplituhedron
• Scattering Forms and the Positive Geometry of Kinematics, Color and the Worldsheet
• Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops
• Into the Amplituhedron
• Positive Geometries and Canonical Forms
• Unwinding the Amplituhedron in Binary
• Tree-level Recursion Relation and Dual Superconformal Symmetry of the ABJM Theory
• Amplitudes and Correlators to Ten Loops Using Simple, Graphical Bootstraps
• Evidence for a Nonplanar Amplituhedron
• The Momentum Amplituhedron
• Dual Superconformal Symmetry of N=6 Chern-Simons Theory
• The Soft-Collinear Bootstrap: N=4 Yang-Mills Amplitudes at Six and Seven Loops
• ABJM amplitudes and the positive orthogonal grassmannian
• Perturbation Theory at Eight Loops: Novel Structures and the Breakdown of Manifest Conformality
• Dualities for Loop Amplitudes of N=6 Chern-Simons Matter Theory
• Conformal Anomaly for Amplitudes in N=6 Superconformal Chern-Simons Theory
• Scattering Amplitudes/Wilson Loop Duality In ABJM Theory
• Light-like polygonal Wilson loops in 3d Chern-Simons and ABJM theory
• One Loop Amplitudes In ABJM
• The Amplituhedron from Momentum Twistor Diagrams
• Cutting Deep Into The Amplituhedron
• 1-loop Amplitudes from the Halohedron
• The Amplituhedron and the One-loop Grassmannian Measure
• Nonperturbative Negative Geometries: Amplitudes at Strong Coupling and the Amplituhedron
• Correlation function of null polygonal Wilson loops with local operators
• Notes on Scattering Amplitudes as Differential Forms
• Grassmannians for scattering amplitudes in 4d $\mathcal{N}=4$ SYM and 3d ABJM
• The m=1 amplituhedron and cyclic hyperplane arrangements
• Parity duality for the amplituhedron
• The orthogonal momentum amplituhedron and ABJM amplitudes
• The momentum amplituhedron of SYM and ABJM from twistor-string maps
• On the ABJM four-point amplitude at three loops and BDS exponentiation
• On correlation functions of Wilson loops, local and non-local operators
• Amplituhedron meets Jeffrey-Kirwan Residue
• All one-loop amplitudes in N=6 superconformal Chern-Simons theory
• Higher loop mixed correlators in N=4 SYM
• All-loop cuts from the Amplituhedron
• Momentum Amplituhedron meets Kinematic Associahedron
• 4-particle Amplituhedronics for 3-5 Loops

Cited by in corpus (7)

• Integrated negative geometries in ABJM
• The Loop Momentum Amplituhedron
• Emergent unitarity, all-loop cuts and integrations from the ABJM amplituhedron
• The two-loop eight-point amplitude in ABJM theory
• Leading singularities and chambers of Correlahedron
• The Aharony-Bergman-Jafferis-Maldacena theory on a circle
• The Geometry of BCFW for ABJM Loop Integrands