Cluster patterns in Landau and Leading Singularities via the Amplituhedron

Understand

We advance the exploration of cluster-algebraic patterns in the building blocks of scattering amplitudes in $\mathcal{N}=4$ super Yang-Mills theory.

• In particular we conjecture that, given a maximal cut of a loop amplitude, Landau singularities and poles of each Yangian invariant appearing in any representation of the corresponding Leading Singularities can be found together in a cluster.
• We check these adjacencies for all one-loop amplitudes up to 9 points.
• Along the way, we also prove that all (rational) N$^2$MHV Yangian invariants are cluster adjacent, confirming original conjectures.