The one-loop amplituhedron is tiled by BCFW cells, extending the author's tree-level proof of the BCFW tiling conjecture to one loop.
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abstract
The (tree) amplituhedron $\mathcal{A}_{n, k, m}$ is introduced by Arkani-Hamed and Trnka in 2013 in the study of $\mathcal{N}=4$ supersymmetric Yang-Mills theory. It is defined in terms of the totally nonnegative Grassmannians. In this paper, we show that the amplituhedron $\mathcal{A}_{n, k, m}$ for $m=2$ admits a triangulation. Our collection of cells is constructed via BCFW-type recursion. We also provide a diagrammatic interpretation of our construction.
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Notes on the one-loop amplituhedron and its BCFW tiling
The one-loop amplituhedron is tiled by BCFW cells, extending the author's tree-level proof of the BCFW tiling conjecture to one loop.