A Note on One-loop Cluster Adjacency in N = 4 SYM

Abstract

We study cluster adjacency conjectures for amplitudes in maximally supersymmetric Yang-Mills theory. We show that the n-point one-loop NMHV ratio function satisfies Steinmann cluster adjacency. We also show that the one-loop BDS-like normalized NMHV amplitude satisfies cluster adjacency between Yangian invariants and final symbol entries up to 9-points. We present conjectures for cluster adjacency properties of Pl\"ucker coordinates, quadratic cluster variables, and NMHV Yangian invariants that generalize the notion of weak separation.