The m=2 amplituhedron

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.

21 pages. Version 2, updated references on the cellular decompositions of totally nonnegative Grassmannians