Amplituhedra and origami

TL;DR

This paper reveals a connection between momentum amplituhedra in physics and origami crease patterns, proving triangulation properties and embedding conditions for planar graphs, bridging geometry, combinatorics, and physics.

Contribution

It establishes a novel correspondence between amplituhedra and origami, and proves new triangulation and embedding theorems for planar bipartite graphs.

Findings

BCFW cells triangulate the momentum amplituhedron with nonnegative Mandelstam variables

Every weighted planar bipartite graph admits a t-embedding with angle sum conditions

The correspondence links geometric structures in physics and origami patterns

Abstract

We establish a precise correspondence between points of momentum amplituhedra and origami crease patterns. As an application, we prove that the BCFW cells triangulate the momentum amplituhedron when all Mandelstam variables are nonnegative. As another application, we show that every weighted planar bipartite graph $\Gamma$ admits a t-embedding, i.e., an embedding of the planar dual of $\Gamma$ such that the sum of angles of white (equivalently, black) faces around each vertex is equal to $\pi$.