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In this paper, we introduce the momentum space amplituhedron for tree-levelscattering amplitudes of ABJM theory. We demonstrate that the scatteringamplitude can be identified as the canonical form on the space given by theproduct of positive orthogonal Grassmannian and the moment curve. Theco-dimension one boundaries of this space are simply the odd-particle planarMandelstam variables, while the even-particle counterparts are "hidden" ashigher co-dimension boundaries. Remarkably, this space can be equally definedthrough a series of "sign flip" requirements of the projected external data,identical to "half" of four-dimensional $\mathcal{N}=4$ super Yang-Mills theory(sYM). Thus in a precise sense the geometry for ABJM lives on the boundary of$\mathcal{N}=4$ sYM. We verify this relation through eight-points by showingthat the BCFW triangulation of the amplitude tiles the amplituhedron. Thecanonical form is naturally derived using the Grassmannian formula for theamplitude in the $\mathcal{N}=4$ formalism for ABJM theory.

The orthogonal momentum amplituhedron and ABJM amplitudes