The ABJM Momentum Amplituhedron -- ABJM Scattering Amplitudes From Configurations of Points in Minkowski Space

Abstract

In this paper, we define the ABJM loop momentum amplituhedron, which is a geometry encoding ABJM planar tree-level amplitudes and loop integrands in the three-dimensional spinor helicity space. Translating it to the space of dual momenta produces a remarkably simple geometry given by configurations of space-like separated off-shell momenta living inside a curvy polytope defined by momenta of scattered particles. We conjecture that the canonical differential form on this space gives amplitude integrands, and we provide a new formula for all one-loop $n$-particle integrands in the positive branch. For higher loop orders, we utilize the causal structure of configurations of points in Minkowski space to explain the singularity structure for known results at two loops.