Evidence for a Nonplanar Amplituhedron

TL;DR

This paper provides evidence that the geometric amplituhedron framework, originally for planar amplitudes, can be extended to nonplanar amplitudes in N=4 super-Yang-Mills theory, revealing similar analytic structures.

Contribution

It demonstrates that the nonplanar sector shares key properties with the planar sector, supporting a potential nonplanar amplituhedron construction.

Findings

Nonplanar amplitudes exhibit dual conformal symmetry.

Logarithmic singularities are present in nonplanar integrands.

Zero residue conditions extend beyond the planar case.

Abstract

The scattering amplitudes of planar N = 4 super-Yang-Mills exhibit a number of remarkable analytic structures, including dual conformal symmetry and logarithmic singularities of integrands. The amplituhedron is a geometric construction of the integrand that incorporates these structures. This geometric construction further implies the amplitude is fully specified by constraining it to vanish on spurious residues. By writing the amplitude in a dlog basis, we provide nontrivial evidence that these analytic properties and "zero conditions" carry over into the nonplanar sector. This suggests that the concept of the amplituhedron can be extended to the the nonplanar sector of N = 4 super-Yang-Mills theory.