The Amplituhedron BCFW Triangulation

TL;DR

This paper proves that the amplituhedron Ank4 can be decomposed into BCFW positroid cells, confirming a conjecture that links geometric structures to scattering amplitudes in quantum field theory.

Contribution

The paper provides a rigorous proof that the amplituhedron Ank4 admits a BCFW positroid cell triangulation, establishing a key geometric understanding of scattering amplitudes.

Findings

Confirmed the conjecture that Ank4 admits BCFW triangulation

Established a geometric decomposition of the amplituhedron

Linked BCFW recurrence to amplituhedron structure

Abstract

The amplituhedron Ank4 is a geometric object, introduced by Arkani-Hamed and Trnka (2013) in the study of scattering amplitudes in quantum field theories. They conjecture that Ank4 admits a decomposition into images of BCFW positroid cells, arising from the Britto--Cachazo--Feng--Witten recurrence (2005). We prove that this conjecture is true.