Boundaries of Amplituhedra and NMHV Symbol Alphabets at Two Loops

TL;DR

This paper classifies the boundaries of amplituhedra relevant for two-loop amplitudes in planar N=4 super-Yang-Mills theory, linking them to branch points and conjecturing the symbol alphabets for NMHV amplitudes.

Contribution

It provides a systematic classification of amplituhedron boundaries at two loops and proposes conjectured symbol alphabets for all NMHV amplitudes based on Landau equations.

Findings

Classified boundaries of amplituhedra relevant for two-loop amplitudes

Determined branch points of all two-loop NMHV amplitudes

Proposed conjecture for symbol alphabets of NMHV amplitudes

Abstract

In this sequel to arXiv:1711.11507 we classify the boundaries of amplituhedra relevant for determining the branch points of general two-loop amplitudes in planar $\mathcal{N}=4$ super-Yang-Mills theory. We explain the connection to on-shell diagrams, which serves as a useful cross-check. We determine the branch points of all two-loop NMHV amplitudes by solving the Landau equations for the relevant configurations and are led thereby to a conjecture for the symbol alphabets of all such amplitudes.