All-Helicity Symbol Alphabets from Unwound Amplituhedra

TL;DR

This paper presents an algorithm to identify branch points in planar N=4 super-Yang-Mills amplitudes using amplituhedra reformulated via sign flips, revealing known and new positivity properties.

Contribution

It introduces a streamlined method to determine branch points for any helicity amplitude using amplituhedra and sign flips reformulation.

Findings

Recovered all known one-loop amplitude branch points.

Discovered emergent positivity on amplituhedron boundaries.

Streamlined algorithm applicable to general amplitudes.

Abstract

We review an algorithm for determining the branch points of general amplitudes in planar $\mathcal{N}=4$ super-Yang-Mills theory from amplituhedra. We demonstrate how to use the recent reformulation of amplituhedra in terms of `sign flips' in order to streamline the application of this algorithm to amplitudes of any helicity. In this way we recover the known branch points of all one-loop amplitudes, and we find an `emergent positivity' on boundaries of amplituhedra.