Cluster patterns in Landau and leading singularities via the amplituhedron

Abstract

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.