Cluster patterns in Landau and leading singularities via the amplituhedron (Q6100162)

Summary: 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) \(\mathrm{N}^2\)MHV Yangian invariants are cluster adjacent, confirming original conjectures.